This page is a companion to the main CDS Invited Lecture Series page. It contains abstracts of lectures from 1996-2005.

## 2004

**Multiagent Repeated Games and convergence to Nash Equilibria**

Jeff Shamma

Mechanical and Aerospace Engineering Department

University of California, Los Angeles

Consider a scenario in which multiple decision making agents repeatedly play a matrix game and adjust their strategies according to observations of each other's actions. The game is noncooperative in that each agent may have its own objective/utility function, and these objectives are not shared among agents. A central issue is whether agent strategies will converge to a Nash equilibrium. Prior work shows how convergence to a Nash equilibrium in this setting may or may not occur. This talk presents new strategic update mechanisms that can lead to convergent behavior in previously nonconvergent cases, such as the Shapley and Jordan counterexamples, through the use of fundamental feedback control concepts.

**Wrinkling, draping and crumpling**

L. Mahadevan

Department of Engineering and Applied Sciences

Harvard University

Bending a thin sheet is easier than stretching it, an observation which has its roots in geometry rather than physics. The consequences of this simple fact allow us to analyze many examples involving the large deformations of thin elastic sheets. I will start by considering the wrinkling of a stretched sheet or of an elephant's trunk, then turn to the aesthetic drapes of a fabric, briefly discuss the intricate folds in origami, and close with a discussion of a violently crumpled sheet that is the fate of many a calculation gone awry.

**Interpolation by rational diffeomorphisms of the circle**

Joel Langer

Department of Mathematics

Case Western Reserve University

The theory of interpolation by rational functions is a highly developed subject, which continues to receive attention---not only because of its intrinsic beauty and mathematical interest, but also because of a variety of applications, e.g., in signal processing, circuit theory, robust stabilization and stochastic control theory. In view of well-known stability criteria, it is not surprising that the modern literature (like the classical Nevanlinna-Pick theory) has dealt with functions whose poles are restricted at the outset to lie in a suitable subdomain. On the other hand, from the point of view of certain geometrical or dynamical considerations, one would like to have techniques for constructing rational circle diffeomorphisms---imposing a rather different analytical condition (while allowing a priori nearly arbitrary pole placement). This talk will present a simple interpolation result in the latter context, and briefly indicate the geometrical origins of the problem.

**System Biology in Practice: Science, Technology, Challenges**

Amir Handzel

Senior Scientist

Beyond Genomics, Inc.

Systems Biology is an emerging and quickly expanding field set to revolutionize biology in the 21st century. Its broad goal is to fully elucidate the dynamics of biological structure and function starting from the molecular level up to the full organism. It also carries far reaching implications for future medical practice including the types of drugs that will be developed and how they will be used. As a harbinger of things to come, for the first time in its history the FDA approved the use of a drug (Herceptin) in conjunction with a genomic test to identify the subpopulation of patients for whom the drug would be effective. In the academic sphere, new dedicated departments and programs are being established. In this talk, I will give an overview of scientific issues and concepts in Systems Biology, and the fast advancing technologies that are enabling its progress. I will describe some associated computational challenges and my recent work to address a few of them.

**Sensor Network Localization**

Brian Anderson

Chief Scientist, National ICT Australia, Ltd

Distinguished Professor, Australian National University

Sensor network localization is the task of establishing the absolute positions of a network of sensors given limited information, such as distances between pairs of close sensors and the positions of a small number of beacon sensors. The question of solvability of the problem can be addressed using concepts of rigid graphs, and in particular the concept of a globally rigid graph, but this concept is much better understood in two dimensions than three dimensions. Actual computation is another matter, and may require calculations growing exponentially or linearly with the number of sensors. Random sensor networks are also considered, where sensors are scattered following some defined law. Conditions ensuring that the network, or most of it, will be localizable, and indeed localizable in linear time, will be described.

**Control Advances in Production Printing and Publishing Systems**

Lalit Mestha Principal Scientist, Wilson Center for Research and Technology

Xerox Corporation

Many digital color printers are based on electro-photographic technology. In the electro-photographic process used for copying and printing, the image content controls the amount of light that selectively discharges a uniformly charged photoreceptor material with a laser or light emitting diodes. The electrostatic image is developed with a charged pigmented thermoplastic powder that is transferred and fused to paper under heat and pressure. Many have already been introduced to the market place and their quality and productivity issues are addressed using optical sensing and modern feedback controls. The integration of computing, imaging, marking and controls technology has created modern color printing & publishing systems, such as the iGen3. In this talk, I will introduce to the multidisciplinary technology from a control system perspective, and then describe the closed loop feedback control systems of key systems which enable the precision color controls and autonomy to digital printing systems.

**Bio-Inspired Robotic Motion Control**

Dimitris Tsakiris

Institute of Computer Science - FORTH

Heraklion, Greece

Control of movement, and its relationship to sensing and perception, is one of the most significant problems for emerging robotic applications dealing with unstructured and tortuous environments. Such problems occur, among other domains, in the endoscopic access to the human body, in site inspection, in search-and-rescue operations in collapsed buildings, even in planetary exploration. Drawing inspiration from biology, where such problems have been effectively addressed by the evolutionary process, can help in overcoming limitations of present-day robotic systems and in designing agile robots, able to adapt robustly to a variety of environmental conditions. This talk will describe work inspired by a class of segmented worms, the polychaete annelids, which offer an intriguing biological paradigm of locomotion on sand, mud, sediment, as well as underwater: the variety of their morphology, sensory apparatus and nervous stem structure is a direct consequence of their adaptation to so diverse habitats. Such locomotion capabilities could benefit, if properly replicated, a robotic system functioning in an unstructured environment. The described work focuses on the use of detailed computational models for the mechanics and bio-inspired motion control of this type of locomotion; these models involve the dynamics of the organism's motion, its interaction with the environment and the neural control of its motion, which is based on central pattern generators. This work has been successful in demonstrating the possibility to generate polychaete-like undulatory gaits, as well as novel undulatory reactive behaviors. An experimental effort is also in progress, aiming at the development of robotic prototypes whose motion is based on polychaete-like undulatory gaits and which are able to propel themselves in an unstructured environment.

**Control Theoretic Aspects of Matrix Factorizations**

Uwe Helmke

Mathematical Institute

University of Wuerzberg

We discuss control theoretic aspects of factorizing elements in a compact Lie group via a given set of generators of the Lie algebra.

Such problems naturally arise in quantum computing and the control of spin systems in nuclear magnetic resonance spectroscopy. We begin with a short introduction on Lie groups and Lie algebras, we discuss relevant controllability issues on Lie groups. The main part of the talk is then devoted to time optimal control and, in particular, to computing time optimal pulse sequences for the control of 2 spin systems.

## 2005

**Measurement and control in quantum information science**

Hideo Mabuchi

Department of Physics and Control & Dynamical Systems

California Institute of Technology

Real-time measurement and feedback control are becoming important tools in quantum information science, with applications ranging from robust entanglement generation to closed-loop precision measurement. Control and dynamical systems theory also have much to contribute to research on fault tolerant schemes for quantum computation and communication. In this talk I will review some of our group's recent experimental and theoretical work in these areas, emphasizing conceptual and methodological synergy with contemporary research in systems and controls.

**Small Brains, Smart Minds: Vision, Navigation and ‘Cognition’ in Honeybees**

Mandyam V. Srinivasan

Centre for Visual Sciences

Research School of Biological Sciences

Australian National University

Insects, in general, and honeybees, in particular, perform remarkably well at seeing and perceiving the world and navigating effectively in it, despite possessing a brain that weighs less than a milligram and carries fewer than 0.01% as many neurons as ours does. Working together with our colleagues, we have been trying to unravel the secrets of their success.

Although most insects lack stereo vision, they use a number of ingenious strategies for perceiving their world in three dimensions and navigating successfully in it. For example, distances to objects are gauged in terms of the apparent speeds of motion of the objects' images, rather than by using complex stereo mechanisms. Objects are distinguished from backgrounds by sensing the apparent relative motion at the boundary. Narrow gaps are negotiated by balancing the apparent speeds of the images in the two eyes. Flight speed is regulated by holding constant the average image velocity as seen by both eyes. Bees landing on a horizontal surface hold constant the image velocity of the surface as they approach it, thus automatically ensuring that flight speed is close to zero at touchdown. Foraging bees gauge distance flown by integrating optic flow: they possess a visually-driven "odometer" that is robust to variations in wind, body weight, energy expenditure, and the properties of the visual environment.

Recent research on honeybee perception and cognition is beginning to reveal that these insects may not be the simple, reflexive creatures that they were once assumed to be. For example, bees can learn rather general features of flowers and landmarks, such as colour, orientation and symmetry, and apply them to distinguish between objects that they have never previously encountered. Bees exhibit “top-down” processing: that is, they are capable of using prior knowledge to detect poorly visible or camouflaged objects. They can navigate through labyrinths by learning path regularities, and by using symbolic signposts. They can learn to form complex associations and to acquire abstract concepts such as “sameness” and “difference”. Bees are also capable of associative recall: that is, a familiar scent can trigger recall of an associated colour, or even of a navigational route to a food location. All of these observations suggest that there is no hard dichotomy between invertebrates and vertebrates in the context of perception, learning and ‘cognition’; and that brain size is not necessarily a reliable predictor of perceptual capacity.

Finally, some of the above principles – especially those that relate vision and navigation – are offering novel, computationally elegant solutions to persistent problems in machine vision and robot navigation. Thus, we have been using some of the insect-based strategies described above to design, implement and test biologically-inspired algorithms for the guidance of autonomous terrestrial and aerial vehicles.

**Optimization and the Price of Anarchy in a Dynamic Newsboy Model**

Sean Meyn

Department of Electrical and Computer Engineering

Coordinated Science Laboratory

University of Illinois at Urbana-Champaign

This seminar concerns resource allocation, pricing, and performance evaluation in electric power markets. The ultimate goal is the integration of new approaches to dynamic control of stochastic networks, with recent results concerning the competitive market equilibrium in network industries, to obtain comprehensive approaches to model reduction and control for network-level bulk power systems.

Described are some modest first steps: a dynamic flow model constructed for a single-consumer model in analogy with a standard stochastic queuing model; the approximation of the socially-optimal policy by an explicit threshold policy; and the inability to sustain the socially-optimal policy as a decentralized market outcome. Generalizations to complex models are also described.

These conclusions have implication to other industries that require high reliability and provide critical services which are undergoing rapid deregulation.

**How Flies Fly**

Michael Dickinson

Department of Bioengineering

Dickinson Lab

California Institute of Technology

A central feature in the natural history and behavior of most insects is the ability to fly through their environment in search of food, shelter, and mates. What physiological and mechanical specializations enable insects to fly stably and orient toward attractive objects? The goal of the research in my laboratory is to `reverse engineer' the flight control system of a fruit fly, and thus determine the means by which the brain and body function collectively to control the animal's trajectory through space. Like all forms of locomotion, flight behavior results from a complex set of interactions, not just within circuits in the brain, but among neurons, muscles, skeletal elements, and physical process within the external world. To control flight, the fly's nervous system must generate a code of motor information that plays out through a small but complicated set of power and steering muscles. These muscles induce microscopic oscillations in an external skeleton that drive the wings back and forth, producing a time-variant pattern of aerodynamic forces that the fly modulates to steer and maneuver through the air. The animal's motion through space alters the stream of information that runs through an array of visual, chemical, and mechanical sensors, which collectively provide feedback to stabilize flight and orient the animal towards specific targets. This research illustrates how processes within the physical world function with neural and mechanical features of an organism's design function to generate complex behavior.

**Control of Systems in a Dimensionless Framework**

Andrew Alleyne

Ralph and Catherine Fisher Professor of Engineering

University of Illinois at Urbana-Champaign

The use of dimensional analysis is prevalent in several fields of the physical and life sciences. In Mechanical Engineering, the common concepts of Fluid Mechanics, Heat Transfer, and Thermodynamics are all represented by dimensionless variables. These include the well known dimensionless numbers such as the Reynolds Number, Froude Number, Nusselt Number, etc. The question we raise and hope to answer in this talk is whether or not the field of Systems and Control can benefit from dimensionless analysis as other fields have done.

This talk will begin by detailing the initiation of our study into dimensional analysis for control systems. Vehicle systems were the primary motivation and several types of planar vehicle systems will be examined. The class of systems under study is LTI systems. We demonstrate the process of taking a dimensional system representation and transforming it into a dimensionless one. It can be shown that the dimensionless form for this linear system can be thought of as a very convenient similarity transformation of the original dimensional system.

Subsequent to presenting a dimensionless form for the dynamics of particular systems, we illustrate several key benefits that we have found from working in a dimensionless framework. First, it is possible to uncover underlying dynamical relationships that do not seem clear when studying the dimensional system dynamics. Secondly, the parametric uncertainty associated with nominal vehicle representations is greatly reduced in a dimensionless framework, thereby leading to less conservative controller constraints for robustness requirements. Finally, parametric interdependence uncovered and can be used to greatly reduce system excitation requirements for identification or adaptation mechanisms. http://mr-roboto.me.uiuc.edu.

## 2002

**H_2/H-Infinity Control of Singularly Perturbed Systems**

K. B. Datta

Department of Electrical Engineering

Indian Institute of Technology, Kharagpur

The lecture provides an introduction to H_2/H_Infinity and mixed H_2/H_Infinity optimal control in linear time-invariant dynamical systems. It will examine the solution of mixed H_2/H_Infinity control of a singularly perturbed system by linear state-feedback with particular reference to model reduction in terms of slow and fast subsystems. Both continuous and discrete time systems are considered. The application areas will be highlighted. It will conclude with remarks on the related future areas of investigation.

**Control of Underactuated Mechanical Systems, or, How to Parallel Park a 10 m Blimp**

Jim Ostrowski

General Robotics Automation, Sensing and Perception (GRASP) Laboratory Department of Mechanical Engineering and Applied Mechanics

University of Pennsylvania

In this talk, I will focus on several aspects of control for underactuated mechanical systems, with emphasis on the specific application of control and motion planning for autonomous airships. I will introduce some important, recently developed tools for mechanical control systems, which rely on affine connections and group symmetries. Emphasis will be given to ways in which these new methods parallel previous concepts in nonlinear control for kinematic systems, and how to generalize previous results to dynamic systems. Experimental results from an indoor blimp will be presented. Finally, I'll conclude with a brief discussion as to how these tools can be formulated within a higher-level motion planning strategy. Using principles from hybrid systems theory, abstractions of lower level dynamics are used to develop simpler control laws at higher levels of planning.

**Geometric strategies for motion planning and coordination**

Francesco Bullo

General Engineering Department

Coordinated Science Lab

University of Illinois at Urbana-Champaign

Motion planning and coordination are key technological problems in the development of dexterous and autonomous robotic systems. This talk presents analysis and design methodologies that build on concepts from nonlinear control theory, and differential and computational geometry. For single vehicle systems, we present a novel controllability notion and its application in planning problems. For multi-vehicle networks, we introduce decentralized control laws for the coordination of multiple agents performing a spatially distributed sensing tasks.

**Modeling Adaptation in Insect Visual Motion Processing**

Patrick Shoemaker

Tanner Research Laboratories

Pasadena, Calif.

It has been known since the early 1980s that adaptation occurs in the neural pathways that detect and process visual motion in insects. Until recently, it was believed that this adaptation was due to adjustment of the time constant of the delay that is an essential feature of the correlational elementary motion detector (EMD), the putative ``front-end'' for all higher-level motion processing. However, convincing evidence has been developed by David O'Carroll of Adelaide University and coworkers that this is not the case and, furthermore, that the primary mechanismn of adaptation is adjustment of contrast gain early in the motion processing pathway. This has interesting implications for the processing performed by EMDs and subsequent motion-sensitive neurons. I describe a collaborative effort with Dr. O'Carroll to model the adaptive EMD in biology and in the medium of analog integrated circuitry.

**Dynamics, Stability and Reduction of Fluctuating Mechanical Systems**

Sri Namachchivaya

Department of Aeronautical and Astronautical Engineering

Nonlinear Systems Group

University of Illinois at Urbana-Champaign

In the first part of my talk, we shall develop mathematical techniques to obtain finite dimensional equations in order to systematically study the mechanism of periodic spindle speed variation for chatter suppression. In the second part of my talk, we shall examine the stationary motion, and stability properties of the stationary motion of a noisy autoparametric system.

**Audiomotor integration for spatially-guided behavior in the echolocating bat**

Cynthia Moss

Department of Psychology

Institute for Systems Research

University of Maryland

The sonar systems of echolocating bats operate through continuous interaction between perception and motor control. The bat actively probes the environment by producing ultrasonic vocal signals that reflect from objects in the path of the sound beam. The bat uses information contained in returning echoes to determine the direction, distance, size and possibly the shape of sonar targets. In turn, the spatial information obtained from sonar echoes guides the aim of the bat's head, direction of its flight path and the acoustic features of its subsequent sonar signals. Many species of bat use echolocation to hunt small insect prey in the dark, a daunting perceptual task, given the acoustic environment in which the bat must operate. To successfully intercept insect prey and avoid obstacles, the bat's sonar system must compute the three-dimensional positions of multiple auditory objects, which are continuously changing with respect to the bat as it flies. The bat's spatial perception of the auditory scene guides its selective control over the acoustic features of its vocalizations, which in turn yield new patterns of sonar echoes that are used to update its behavior. My talk will focus on perception and action for spatially-guided behavior in the echolocating bat. I will present data from insect capture studies that detail the bat's control over its flight path, head aim and sonar vocalizations. The data from these studies reveal distinct temporal patterns in the bat's sonar signal production that occur with target selection and interception, as well as obstacle avoidance. In addition, I'll describe neurophysiological studies of the superior colliculus of the bat, a midbrain structure implicated in orienting behavior. In particular, I will present data suggesting that the superior colliculus of the echolocating bat shows specializations to support audiomotor integration for acoustic orientation by sonar.

**Linguistic control of mobile robots**

Magnus Egerstedt

Department of Electrical and Computer Engineering

Georgia Institute of Technology

When humans give each other directions only tokenized, linguistic instructions are used. In contrast to this, classic control theory relies on the ability to specify a control action at each time instant. In this talk, a linguistic control theory will be presented, based on the motion description language formalism, and the interactions between symbolic (computer generated) instructions and mechanical devices will be given a hybrid representation. A complexity measure will furthermore be defined on the input strings that measures the number of bits needed for coding the instructions. This measure serves as a novel tool for studying optimal coding strategies, as well as sensor and actuator selections for mobile robots, thus providing a unified framework in which a number of questions in robotics can coexist.

**Some issues in the control of distributed/stochastic systems**

Yannis Kevrekidis

Department of Chemical Engineering

Program in Applied and Computational Mathematics

Princeton University

I will discuss recent results in two directions. The first involves control in distributed, pattern forming systems with finely resolved sensing and actuation. There will be extensive experimental results from catalytic reactions on laser microaddressable catalyst surfaces. Supporting modeling/computations will also be presented. The second direction involves what we call "coarse control" of atomistic systems. An "equation-free" methodology for performing controller design computations directly based on microscopic/stochastic simulators will be presented. This approach sidesteps the necessity of obtaining macroscopic governing equations in closed form.

**Dynamics and Controls of Formation Flying Satellites in Earth Orbits**

Sesha Sai Vaddi

Department of Aerospace Engineering

Texas A&M University

Formation flying of satellites is an upcoming technology suitable for applications like SAR and space based interferometry. In this research we have analyzed different issues related to the dynamics and control of formation flying satellites. A typical formation consists of a central chief satellite swarmed by multiple deputy satellites. Bounded relative orbits between the chief and deputy are essential for formation flying. Hill's equations offer attractive solutions to the relative motion dynamics of two satellites. But these solutions break down due to the nonlinear effects of the differential gravity accelerations, eccentricity of the chief orbit and other perturbations to the two-body problem like the oblateness of the Earth. We analyze the effect of each of the above-mentioned perturbations and suggest corrective measures that prevent the breakdown. Fuel-efficient control schemes that exploit the natural solutions of the relative motion dynamics will be presented. A fuel balancing control scheme is derived for homogenizing the fuel consumption by different satellites in the formation. Some preliminary results on the formation reconfiguration problem will also be discussed.

**A Generative Theory of Shape**

Michael Leyton

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Rutgers University

Generative theory of shape has two properties regarded as fundamental to intelligence - maximizing transfer of structure and maximizing recoverability of the generative operations. These two properties are particularly important in the representation of complex shape. The primary goal of this theory is the conversion of complexity into understandability. For this purpose, a mathematical theory is presented of how understandability is created in a structure. This is achieved by developing a group-theoretic approach to formalizing transfer and recoverability. To handle complex shape, a new class of groups is developed, called unfolding groups. These unfold structure from a maximally collapsed version of that structure. A principal aspect of the theory is that it develops a group-theoretic formalization of major object-oriented concepts such as inheritance. The result is an object-oriented theory of geometry. This talk will address the theory presented in his latest book, A Generative Theory of Shape.

**Invariant Subspace Computation—A Geometric Approach**

Pierre-Antoine Absil

Department of Electrical Engineering and Computer Science

Institut Montefiori

University of Liege

The theme of this presentation is eigenspace computation, an ubiquitous task in engineering and physical sciences. More precisely, we consider the problem of iteratively refining estimates of an eigenspace of an n-by-n data matrix. This problem nicely lends itself to a geometric approach, since the iterates belong to a particular non-Euclidean set, the set of fixed-dimensional subspaces of Rn, commonly referred to as the Grassmann manifold. In order to derive numerical algorithms from the geometric approach, it is essential to understand the relation between the geometric objects (subspaces) and the numerical representations of these entities. It turns out that matrix representations of subspaces admit a topological structure of GL-principal fiber bundle over the Grassmann manifold. Interestingly, a similar structure appears in several other problems, including linear systems realization. In this talk, we will present two recently proposed numerical algorithms that stem from this Grassmannian approach. The first one is a Newton method that relies on the Riemannian geometry of the Grassmann manifold. It converges locally quadratically to the eigenspaces of the data matrix, and even cubically when the data matrix is symmetric. The second algorithm is a generalization to the Grassmann manifold of the classical Rayleigh quotient iteration. The new iteration converges locally cubically to the eigenspaces of a symmetric data matrix, and a two-sided version is proposed for tackling the nonsymmetric case. This is work was done in collaboration with Rodolphe Sepulchre (University of Liege, Belgium), Robert Mahony (Australian National University) and Paul Van Dooren (Universite Catholique de Louvain, Belgium).

## 2003

**Drive-by Sensing: Lessons Biology Can Teach Robots**

Roman Kuc

Intelligent Sensors Laboratory

Department of Electrical Engineering

Yale University

Many biological sensing systems, such as humans and bats, scan their environment while moving, which we term drive-by sensing. This would be a desirable mode in robotics if sufficient information were acquired. This talk describes a novel scanning method motivated by acoustic flow to recognize objects directly from sonar. Right-angle corners and large-diameter cylinders form specular retro-reflectors that produce strong echoes whose features can be identified. A multi-point sonar produces a point process, temptingly analogous to biological action potentials, whose density encodes the echo amplitude. As an obliquely-oriented sonar beam passes over a retro-reflector, a sequence of strong echoes exhibits a pattern predicted by a forward model. A conventional Polaroid 6500 ranging module produces 5,000 sonar points in a drive-by scan of a hallway, which an algorithm converts into 6 corner locations. Directly recognizing objects from echoes extends sonar sensing from data acquisition to landmark identification for robot navigation.

**Control of Multi-Robot Systems**

Vijay Kumar

GRASP Laboratory

University of Pennsylvania

This talk will address cooperative control of networked robots equipped with cameras. We will first show how decentralized control policies can be used to achieve desired formations while maintaining constraints arising from communication and sensing. We will derive measures of performance for the networked system and show how the formation can be adapted to maximize performance. These results will be illustrated with our experimental testbed of mobile robots. Time permitting, we will address ongoing work on modeling and controlling biomolecular networks and discuss some similarities with the multirobot control problem.

**Controller Design for a Five-Line Planar Biped Robot**

Jessy W. Grizzle

Control Systems Laboratory

EECS Department

University of Michigan

This presentation will discuss controller analysis and design for the walking motion of a 5-link planar biped robot equipped with four actuators: two at the hips acting between the torso and each femur and one at each of the knees, with no actuation at the ankles. The system is thus underactuated. Moreover, the robot’s model is hybrid in nature, assuming a rigid contact when the swing leg impacts the ground and an instantaneous double-support phase. It will be shown how to reduce the stability analysis and performance enhancement aspects of the controller design to a one-degree of freedom dynamical system. Experimental collaboration of the principal results will be presented. The talk will be amply illustrated with pictures, animations and videos in place of formal proofs, which are available in various papers: http://www.eecs.umich.edu/~grizzle/

**Why Be Backward? Forward Evolution Equations for Barrier Options**

Ali Hirsa

Morgan Stanley, New York

Abstract not available. This lecture is presented as part of the ISR Systems Seminar Series.

**Juggling dynamics and a billiard control problem**

Rodolphe Sepulchre

Department of Electrical Engineering and Computer Science

University of Liege

Juggling serves as a remarkable benchmark for cross-disciplinary studies of complex animal tasks that involve rhythm and coordination. The task is complex enough to retain central issues and simple enough to allow for mathematical analysis. Often precursors of hopping or walking robots, impressive juggling machines have been built during the last decade. Yet the theoretical understanding of their dynamical behavior has remain limited.

This talk will introduce a stabilization problem for periodic orbits in a wedge billiard, the simplest mathematical model of a planar juggler. Starting with the rich dynamical behavior of the uncontrolled wedge billiard, we will illustrate the derivation of stabilizing control laws of some unstable periodic orbits. We will also discuss the minimal feedback information needed to achieve stabilization of these impact control systems and some related open issues.

**Stability of Phase Locking Behavior of Coupled Oscillators **

Dirk Aeyels

University of Ghent, Belgium

We study a network of all-to-all interconnected phase oscillators as given by the Kuramoto model. For coupling strengths larger than a critical value, we show the existence of a collective behavior called phase locking: the phase differences between all oscillators are constant in time.

Necessary and sufficient conditions for the existence of phase locking behavior are given. Moreover, the local stability properties of all phase locking solutoins is examined and it is proved that for a sufficiently large coupling strength there exists just one phase locking solution which is locally asymptotically stable.

This type of behavior is different from the partial synchronization behavior described in the literature for a continuum of oscillators, where only a subset of the oscillators is phase locked.

**Towards Flapping-of-Wings Flight of a Butterfly from Robotic Controls**

Kei Senda

Department of Mechanical Systems Engineering

Kanazawa University

This talk is composed of two parts: the flapping-of-wings flight of a butterfly and the robotic control using a neural oscillator and modulator. The former is conducted as a preliminary study for biologically inspired robotics. The latter illustrates how this robotic engineer realizes a robotic controller using a neural oscillator.

The first part discusses flapping of wings of a butterfly, which is rhythmic and cyclic motion. The objective of this part is to clarify the principle of a stable flapping-of-wings flight. First, a dynamics model of a butterfly is derived for analyses by Lagrange's method, where the butterfly is considered as a rigid body system. Second, a simple method and a vortex method are applied to make a simulator where the methods calculate the aerodynamic force. Next, an experimental system with a low-speed wind tunnel is constructed for fundamental data of flapping-of-wings motion, where the system measures the aerodynamic force and the motion simultaneously by a balance and an optical measurement system. Validity of the mathematical model is examined by comparing the measured data with the numerical results. A periodic orbit of a flapping-of-wings flight is searched so as to fly the butterfly model. Furthermore, numerical computation examines the stability of a flapping-of-wings motion generated by a neural network oscillator.

The latter part presents two methods to generate rhythmic and cyclic motions observed in insects by using oscillators and modulators. The proposed methods enable to specify the approximation accuracy of the generated trajectory to the target one even though typical recurrent neural networks cannot. One of the methods is a Fourier series method based on a nonlinear oscillator generating sinusoidal motion and the Fourier series. The other is a modulation method based on a recurrent neural network oscillator and a layered neural network modulator. The realized dynamics has the desired trajectory as a limit cycle. The modulation method can store some trajectories in a network, which is suitable for feedback control design. This study derives controls containing the proposed methods for a space robot, where the system is under a nonholonomic constraint of the angular momentum conservation. The effectiveness of the proposed methods is examined by numerical simulations of reorientation of the space robot using a cyclic motion of the manipulator and/or a feedback control.

**Stability of Networked Control Systems in the Presence of Packet Losses**

Babak Azimi-Sadjadi

Department of Electrical, Systems and Computer Engineering, Rensselaer Polytechnic Institute

Institute for Systems Research, University of Maryland

Networked control systems are systems whose sensors, actuators, estimator units, and control units are connected through communication networks. This type of system has the advantage of greater flexibility with respect to traditional control systems. Also, it allows for reduced wiring, as well as a lower installation cost. It also permits greater agility in diagnosis and maintenance procedures.

Unlike stand-alone control systems, in networked control systems the synchronization between different sensors, actuators and control units is not guaranteed. Furthermore, there is no guarantee for zero delay or even constant delay in sending information from sensors to the control units and control signals from the control units to the actuators. When there is congestion in the communication networks, some packets are dropped to either reduce the queue size in the path or to inform the senders to reduce their transmission rates. In real time systems, particularly control systems, delays or dropped packets may be catastrophic and may cause instability in the control system.

In this talk we present a general framework for networked control systems, where all components are assumed to be connected through a communication network. We consider network delay in our analysis only inasmuch as it relates to dropping packets due to an extensive delay, and the effect of this on the stability of the system. We use the uncertainty threshold principle to show that under certain conditions there is a rate for dropped packets for which an undisturbed networked control system is mean square stable.

**Modeling the cell's sense of direction**

Pablo Iglesias

Department of Electrical and Computer Engineering

Center for Computational Medicine and Biology

The Johns Hopkins University

Many biological systems have the ability to sense the direction of external chemical sources and respond by polarizing and migrating toward chemoattractants or away from chemorepellants. This phenomenon, referred to as chemotaxis, is crucial for proper functioning of single cell organisms, such as bacteria and amoebae, as well as multi-cellular systems as complex as the immune and nervous systems. Chemotaxis also appears to be important in wound healing and tumor metastasis. A common feature of most chemotactic signaling systems is the ability to adapt to different levels of external stimuli, so that it is the gradient of signaling molecule rather than the average signal value that determines the response. Chemotactic cells exhibiting perfect adaptation respond to spatially homogeneous increases in external stimulus by transient activation of specific intracellular signaling pathways. The same signaling pathways, however, can be activated persistently if the signal is presented in a spatially inhomogeneous, graded manner. Recently there has been much effort in trying to elucidate the mechanism used by cells to perceive this external gradient. In this talk I present a model in which the cellular response is regulated by the balance between a fast, local excitation signal and a slower, global inhibitor. I will show how the model makes distinctive predictions that differentiate it from other published models. Finally, I will discuss experimental efforts used to validate this model.

**On the Optimal Control of Hybrid Systems: Theory and Algorithms for Trajectory and Schedule Optimization**

Peter Caines

Department of Electrical and Computer Engineering

McGill University

Hybrid systems have state spaces with both continuous and discrete subspaces and correspondingly continuous and discrete dynamics; they appear in a vast range of contemporary engineering systems with some examples being given by chemical engineering and manufacturing plants, and aerospace and automotive control systems. In work with Shahid Shaikh, we formulate a general class of hybrid system optimal control problems (HOCPs), and provide a Hybrid Maximum Principle (HMP) and a Hybrid Dynamic Programming theory. Efficient HMP based HOCP algorithms are presented with proven convergence properties. The work to this point assumes that the sequence of discrete states (i.e. the schedule) is fixed while the switching times and corresponding continuous switching states, and the continuous controls are to be optimized. We next introduce the notion of Optimality Zones(OZ) which permits one to reach the global optimum with respect to the schedules as well as the continuous decision variables with computational complexity which is only linear in the number of switching times. It is hoped that the OZ notions will lead to a differential and algebro-geometric analysis of HOCPs. Computational examples will be presented.

**Computational Anatomy and Models for Image Analysis**

Michael I. Miller

Director, Center for Imaging Science

The Johns Hopkins University

Recent years have seen rapid advances in the mathematical specification of models for image analysis of human anatomy. As first described in "Computational Anatomy: An Emerging Discipline", Grenander and Miller, Quarterly of Applied Mathematics, Vol. 56, 617-694, 1998, human anatomy is modelled as a deformable template, an orbit under the group action of infinite dimensional diffeomorphisms. In this talk, we will describe recent advances in CA, specifying a metric on the ensemble of images, and examine distances between elements of the orbits, "Group Actions, Homeomorphisms, and Matching: A General Framework", Miller and Younes, Int. J. Comp. Vision Vol. 41, 61-84, 2001, "On the Metrics of Euler-Lagrange Equations of Computational Anatomy, Annu. Rev. Biomed. Eng., Vol. 4, 375-405, 2002. Numerous results will be shown comparing shapes through this metric formulation of the deformable template, including results from disease testing on the hippocampus, and cortical structural and functional mapping.

**Temporal logic control of continuous systems**

George Pappas

Department of Electrical and Systems Engineering

University of Pennsylvania

Embedded systems, which merge information systems with physical systems, are ubiquitous. Computational systems operating in parallel with dynamical or control systems give rise to tremendous modeling and design challenges for the modern engineer. On one hand, control theory has historically focused on properties such as stability, controllability, and optimality. Advances in control theory usually focused on the complexity of the model, but not the complexity of the specification. Embedded systems require very novel, very challenging specifications that have to deal with synchronization, sequencing, and temporal ordering of different tasks. Mathematically formulating such desired specifications cannot be naturally described using traditional formulations in control theory. On the other hand, concurrency theory and formal verification have popularized the use of several temporal logics such as Linear Temporal Logic (LTL), and Computation Tree Logic (CTL) to describe such complex specifications. However, the emphasis has been on verification of these properties for purely discrete systems, and not on synthesis for systems with a continuous component.

In this talk, I will present an algorithmic approach for automatically synthesizing hybrid controllers for continuous systems in order to satisfy specifications that are expressed in temporal logics. In particular, given a controllable linear system, and a finite set of predicates in a special form, we present an algorithm that extracts a property-dependent, finite abstraction which is equivalent (bi-similar) to the original control system. This enables the use of algorithmic procedures for controller synthesis based on powerful automata theoretic techniques, bridging a semantic gap between control theoretic models and computer science specifications. The discrete controllers for the abstracted model are then formally refined to hybrid controllers for the original control system that are formally correct by construction. A Matlab implementation receives as inputs a control system, the temporal logic formula, and automatically generates a StateFlow/Simulink supervisor.

This is joint work with Paulo Tabuada and George Fainekos.

## 2000

**A comparison of the rigid body equations and the incompressible, inviscid ideal fluid flow equations, with the extremals of two optimal control problems**

Peter E. Crouch

College of Engineering and Applied Sciences

Arizona State University

In collaboration with Anthony M. Bloch, Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu

In this talk, we describe two dynamical systems, related to the generalized rigid body equations and the incompressible, inviscid fluid flow equations, that are obtained as the extremal flows of two optimal control problems. We then discuss the relations between these extremal flows and the classical systems. These relations yield new insights into the classical systems, including seemingly new Hamiltonian representations for both systems. If there is time, the Moser-Veselov discretization of the rigid body equations will be derived from a corresponding optimal control problem, exhibiting the same structure as the continuous time analog.

**Nonlinear Dynamics and Control of Fluid with Applications to Turbomachinery**

Richard M. Murray

United Technologies Research Center

This talk will provide a survey of some of the nonlinear dynamics and control problems that arise in the context of turbomachinery, primarily motivated by gas turbine engines for propulsion and power. By making use of reduced order models and control-orineted nonlinear analysis techniques, substantial progress has been made in understanding and actively controlling fluid instabilities in these systems. Specific results include stabilization of rotating stall and surge in axial flow compression systems and control of combustion instabilties in lean, pre-mixed industrial power systems. Nonlinearity plays an integral role in both the dynamics and control of these systems and non-equilibrium behavior (e.g., stable and unstable limit cycles) must be exploited. Analytical results on bifurcation control in the presence of magnitude and rate limits give insights into some of the fundamental performance limitations in active control of this class of fluid instabilities. Experimental results on a low speed, axial flow compressor and a full-scale industrial combustion rig will be used to illustrate the combined role of dynamic modeling and analysis with active control technology.

**Audio and Video Signal Acquisition in Challenging Environments: Current Research at the Harvard Intelligent Multi-Media Environments Laboratory (HIMMEL)**

Michael Brandstein

Division of Engineering and Applied Sciences

Harvard University

The overall goal of the research at the Harvard Intelligent Multi-Media Environments Laboratory (HIMMEL) is to produce automated and relevant high-quality signal capture in noisy enclosures which have been populated with remote microphones and video cameras. This process should be achieved without the active participation or distraction of its human users. This talk will focus on two projects currently underway at HIMMEL. The first deals with the multi-channel enhancement of speech degraded by reverberations and additive noise. We will discuss our work to incorporate speech modeling into the multi-channel context as opposed to addressing the problem strictly from a beamforming or inverse filtering perspective. This approach is shown to be capable of attenuating multipath effects without requiring explicit estimation of room channel responses. We will then present the results of work currently underway for real-time tracking of faces using a combination of acoustic and visual cues. Initial talker locations are estimated acoustically from microphone array data while precise localization and tracking are derived from image information. The system is capable of tracking multiple individuals simultaneously and is robust to nonlinear source motions, complex backgrounds, varying lighting conditions, and a variety of source-camera depths.

**Models of Insect Locomotion: Why Cockroaches Get Away**

Philip Holmes

Department of Mechanical and Aerospace Engineering

Program in Applied and Computational Mathematics

Princeton University

I will discuss joint work with John Schmitt in which we study the dynamics and stability of legged locomotion in the horizontal plane. Inspired by experimental studies of insects due to R.J. Full, et al., we develop two and three-degree-of freedom rigid body models with both rigid 'peg-legs' and pairs of elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed 'muscle' forces, leg displacements and combined strategies. The resulting (piecewise-holonomic) mechanical systems exhibit periodic gaits whose neutral and asymptotic stability characteristics are due to intermittent food contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and relative body orientation. We discuss the relevance of our idealized models to recent experiments and simulations on insect running and turning, and argue that our models may help understand the scaling of gait characteristics over a wide range of animal types and sizes.

**Active Shielding and Control of Environmental Noise**

Josip Loncaric

Institute for Computer Applications in Science and Engineering

NASA Langley Research Center

We present a mathematical framework for the active control of time-harmonic acoustic disturbances. Our approach provides for the exact volumetric cancellation of unwanted noise in a given predetermined region of space while leaving the rest of the total acoustic field unaffected. For eliminating the unwanted component, one needs to know neither the actual noise sources nor properties of the supporting medium. The controls are built based solely on the measurements performed on the perimeter of the region to be shielded; moreover, the controls themselves are concentrated also only near this perimeter. The measured quantities can refer to the total acoustic field, and the methodology automatically distinguishes between its adverse and friendly components. We construct a closed form general solution to the aforementioned noise control problem. The apparatus used for deriving this general solution is closely connected to the concepts of generalized potentials and boundary projects of Calderon's type. For a given total wave field, the application of the Calderon's projection allows us to decompose it into the incoming and outgoing components with respect to a particular domain of interest, which may have arbitrary shape. Then, the controls are designed so that to suppress the incoming component for the domain to be shielded or alternatively, the outgoing component for the domain, which is complementary to the one to be shielded. To demonstrate that the new noise control technique is appropriate, we analyze a simple two-dimensional model example that allows full analytical consideration.

**Nonlinear Model Reduction: Control and Computational Mechanics**

Jerrold E. Marsden

Division of Engineering and Applied Science

California Institute of Technology

This talk will present some recent advances in the theory of model reduction and its relations to the Karhunen-Loeve method for mechanical systems and systems with symmetry. The use of this methodology in control problems and for computational mechanics will be discussed.

**Low Energy Routes Using Chaos in Space Travel and Astronomy**

Edward Belbruno

Program in Applied and Computational Mathematics

Princeton University

Over the past two decades, a new type of chaotic motion was noticed in celestial mechanics that was little understood. In 1987, the speaker was able to find a numerical way to estimate this chaos and to apply it to finding very low energy pathways that spacecraft can follow, for example from the earth to the moon. This approach, now called WSB (weak stability boundary) theory, was validated by being operationally demonstrated in 1991 when it produced a new low energy route to the moon, used to enable the Japanese spacecraft Hiten to reach the moon in October of that year. Since then this approach has evolved considerably, and is being used for a number of new missions including Japan's Lunar-A and PLANET B, and ESA's SMART-1. It is also being used in the Europa mission study at JPL. An interesting application of WSB theory involves the subject of resonance jumping comets, with Brian Marsden at Harvard, and Edgeworth-Kuiper belt objects. Some new work by Jerrold Marsden and his colleagues at Caltech/JPL is discussed in relevance to WSB motions. Also discussed is the 'invariant manifold' approach to halo orbit station keeping as another way of using chaos. A new analytic approach to estimating the WSB is presented which is very interesting. If there is time, some new theoretical work of Hill's problem will be mentioned.

**Engineering Applications of Noncommutative Harmonic Analysis**

Gregory S. Chirikjian

Department of Mechanical Engineering

Johns Hopkins University

Noncommutative harmonic analysis is an area of mathematics that is a generalization of classical Fourier analysis. A goal in noncommutative harmonic analysis is to expand functions on certain kinds of Lie groups in terms of irreducible unitary representations. Another goal is to examine how differential operators acting on functions on Lie groups are transformed into algebraic operations in generalized Fourier space. This is a form of operational calculus.

In this talk, techniques of noncommutative harmonic analysis applied to the group of rigid-body motions, SE(3), are used in the context of robotic manipulators and polymer chains. It is shown how probability density functions describing the relative position and orientation of one end of a manipulator (or polymer chain) can be generated using the techniques. Issues such as self-avoidance and applications of FFTs for groups will also be discussed.

**Patterns and their dynamics in catalytic CO oxidation**

J. Krishnan

Department of Chemical Engineering

Princeton University

The catalytic oxidation of carbon monoxide on Pt(110) single crystal surfaces reveals a wide variety of spatiotemporal patterns. The length scale of these patterns is of the order of microns and they have been observed experimentally using Photo Emission Electron Microscopy. These patterns arise from the interplay of non-linear reaction and diffusional transport of the adsorbed species, and are modeled by reaction-diffusion equations of the activator-inhibitor type.

In this talk, we will focus on specific non-linear patterns and their dynamics. In these cases, the solution is not known in closed form, and therefore numerical methods are necessary. The PDE is discretized in space to yield a large dimensional dynamical system. Bifurcation analysis and numerical simulation are used to study this system.

The first problem to be considered is the dynamics of solitary pulses travelling with constant speed in 1-D. These are analyzed as steady states of the PDE in the co-moving frame. These undergo a variety of instabilities ranging from oscillatory instabilities to ``backfiring''. Then, motivated by experiments, we shall discuss rotating pulse-like structures in thin annular domains. In this case the pulse shape and speed vary depending on the location of the pulse in the annulus. This is because the diffusion of the adsorbed species on the underlying surface is anistropic. In the thin annulus limit, the problem can be reduced to a 1-D problem in a heterogeneous medium. We study the dynamics and instabilities of these rotating pulses. Since their shape and speed vary, numerical Floquet analysis is employed to determine their stability. Finally, we study the instabilities of a 1-D version of a target pattern in this system. Some of the instabilities seen here are also observed in other distributed chemical systems.

**Using Attractor Dynamics to Generate Autonomous Robot Behavior**

Gregor Schoener

Centre de Recherche en Neruosciences Cognitives

Marseille, France

Generating simple motor behaviors in autonomous robots requires more than classical control. Simple forms of decision making are needed. The idea to use nonlinear attractor dynamics to achieve both stable behavior and decision making was originally motivated by analogies with nervous systems. The main ideas are reviewed and their implementation in a simple autonomous vehicle is illustrated. The method is compared to the potential field approach. The need for "neural" representation is identified and an outlook to problems of estimation and fusion is provided.

**Schooling Autonomous Vehicles with Artificial Potentials**

Naomi Ehrich Leonard

Department of Mechanical and Aerospace Engineering

Princeton University

We describe distributed control laws that are designed to allow a group of autonomous vehicles to perform maneuvers that resemble schooling or flocking. Natural schools and flocks are notable for their remarkable capacity to display highly organized group-level behaviors; the group exhibits an "emergent intelligence" that arises from individual-level behaviors. For our group of vehicles, we govern individual-level behavior with control laws that derive from artificial potentials. Artificial potentials are defined to model the desired local interaction between neighboring vehicles and the interaction between each vehicle and a fictitious mission leader. The corresponding interaction forces maintain inter-vehicle spacing and enforce inter-vehicle orientation alignment so that schooling behavior can emerge. A Lyapunov function is constructed from the artificial potentials for analysis of the closed-loop, multiple-vehicle system dynamics. We apply these ideas to the case of autonomous underwater vehicle schooling, and describe the multiple underwater vehicle experimental test-bed that we are developing at Princeton.

## 2001

**Time Optimal Control of Quantum Systems **

Navin Khaneja

Dartmouth College

The last 50 years have witnessed a steady increase in our ability to manipulate and control phenomenon at quantum level. The revolution that began with spectroscopy has culminated in recent advances showing the possibility of harnessing quantum dynamics for processing, protecting and storing information. A central problem in the design of quantum information processors and coherent control of quantum phenomenon in general is the phenomenon of decoherence. It is therefore of utmost importance to control these systems in a time optimal manner before decoherence corrupts the system of interest. In this talk we will focus on the time optimal control of nuclear spins in NMR quantum computing and spectroscopy. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. We will give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. From a general control theory perspective, the problems we want to study have the following character: Suppose we are given a controllable right invariant system on a compact Lie group; what is the minimum time required to steer the system between points of interest.

**Control Techniques for Platoons of Underwater Vehicles**

Bradley E. Bishop and Daniel J. Stilwell

United States Naval Academy

In this talk, cooperating professors present methods for control of cooperating robots, consisting of two convergent methods for the control of platoons (or swarms) of cooperating autonomous underwater vehicles. The two distinct techniques that will be presented approach the problem from opposite directions, first asking what we can hope to accomplish with fully centralized control and then focusing on techniques for generating decentralized controllers that will approach the performance of a centralized scheme.

We initially cast the vehicle platoon as a redundant manipulator, allowing us to bring to bear all of the well-established tools of redundant manipulator control to assist in real-time motion planning and formation synthesis. We develop a novel technique for optimizing the null space of the platoon Jacobian function so that secondary tasks can be achieved with locally maximal system resources. This fundamentally new approach to platoon modeling allows us to build sophisticated centralized platoon behaviors based on sound control theoretic techniques without the necessity for off-line motion planning, nor even advanced computational capabilities.

We then present basic results on the use of decentralized control theory to aid in understanding how platoons of vehicles might cooperate underwater. Of fundamental importance to our work is the severely limited communications channel available underwater. We highlight a particular solution that arises from the decentralized control framework: a broadcast-only communications structure in which the total communications bandwidth is independent of the number of vehicles in the platoon.

**Parameter Estimation with Vision and Range**

Bijoy Ghosh

Department of Systems Science and Mathematics

Washington University

The problem of estimating the structure of objects moving relative to a camera and a laser range finder, has been the subject matter of great interest for well over two decades with applications in mobile robotics and aerospace. To study this class of estimation problem, the role of a homogeneous dynamical system will be emphasized leading to a criterion as to what extent parameters can be identified. Dynamics of feature points, lines and algebraic curves in space, all has this flavor with varying degree of complexity. Overall, this talk emphasizes the role of dynamical systems theory in mobile robotics and machine vision.

**Asymptotic Stabilization of Relative Equilibria**

Thomas Posbergh

University of Minnesota

The application of fundamental methods of theoretical mechanics to nonlinear control problems has led to new methods and insights into the solution of such problems over the last decade. In this talk we will discuss recent work in this area on the asymptotic stabilization of relative equilibria. The objective in this case is the stabilization of steady motion and the design of a feedback control scheme that leaves invariant a subset of conserved quantities of the system. Our viewpoint is that of mechanical systems with symmetries. The theory will be discussed in the context of specific examples including a rotating rigid body and an asymmetrical heavy top.

**Controlling the central pattern generator locomotion after spinal cord injury: Problems and solutions**

Avis Cohen

Neuroscience and Cognitive Sciences

Institute for Systems Research

University of Maryland

Many years ago, my colleagues and I presented evidence that a larval lamprey with a spinal transection can recover full and normal function. (The larval lamprey is a stable life phase of 3-5 years) We now can show that the functional status of the animal depends on the temperature at which the animal recovers from its injury. At room temperature, it is more likely than not to recover full function. However, at its normal coldroom temperature, it is more likely to develop dysfunctional behavior patterns. It appears that one problem is that serotonin does not regenerate properly in any of the injured animals. I will present the data from these studies and an hypothesis regarding why this might be involved in the dysfunctional behavior. Thus, regeneration even in this primitive vertebrate can be problematic, despite the fact that it regenerates spontaneously. Indeed, its best recovery is not under its normal conditions. These results suggest that regeneration in humans is, therefore, likely to require considerably more work in order to obtain full functional recovery. Consequently, we have begun to consider the use of neuroprosthetic devices based on neuromorphic engineering principles to aid spinal cord injury patients. As a first step, I will present data from work done in collaboration with Ralph Etienne-Cummings, Anthony Lewis and Mitra Hartmann demonstrating that an analog VLSI chip can control a pair of legs in a way similar to that offered by the spinal pattern generator for locomotion including responses to sensors to adaptively control the step cycle.

**High-resolution optical wave front sensing and control**

Eric Justh

Institute for Systems Research, University of Maryland

Intelligent Optics Laboratory, Army Research Lab

A coherent optical beam passing through the atmosphere is subject to wave-front distortion: thermal gradients in the air produce index-of-refraction variations, and hence optical path-length variations, over the cross-section of the beam. Adaptive optics is the discipline concerned with real-timecompensation of such wave-front distortion, and has had major impact, e.g., inastronomical imaging. In conventional adaptive optic systems, wave-front correction is achieved using a deformable mirror (with at most several hundred degrees of freedom) to cancel the wave-front distortion. A wave-front sensor capable of measuring the residual distortion is also required, and the challenge is that optical wave front, or phase, can be measured only indirectly. In conventional systems, spatial derivatives of the wave front are measured, and numerical techniques are used to, in effect, reconstruct the wave front from the spatial derivative measurements.

Recent advances in high-resolution spatial light modulators (SLMs) based onliquid-crystal and microelectromechanical (MEMS) devices have opened up the possibility for high-resolution wave-front sensing and control (with 10^4 degrees of freedom for wave-front correction). However, in addition to the devices, there is also a need for control laws which scale appropriately for the high-resolution regime. In recent work arising from a collaboration between the ISR and the Army Research Lab, we have analyzed and demonstrated a control scheme appropriate for high-resolution adaptive optics. Inexpensive, high-speed, high-resolution wave-front control has potential applications in imaging (both astronomical and terrestrial), point-to-point laser communications, laser radar, phase-contrast microscopy, and directed-energy applications.

This talk primarily describes the modeling, analysis, and experimental work on the high-resolution wave front sensing and control system developed jointly with Professor P.S. Krishnaprasad at the University of Maryland and Dr. Mikhail Vorontsov and his group at the Intelligent Optics Laboratory at the Army Research Laboratory in Adelphi, Maryland.

**Modeling and Control of Thin Film Deposition**

Martha Gallivan

Department of Mechanical Engineering

Control and Dynamical Systems

California Institute of Technology

Thin film deposition is an industrially-important process that is critical in the manufacture of integrated circuits and MEMS devices. As the size of integrated circuits shrinks and material complexity grows, the empirical approach to process design is becoming increasingly difficult. A systematic, model-based approach for the intelligent design of time-varying process parameters may provide an alternative to the current trial-and-error method. Viewing thin film deposition as an input-output system, with process parameters as inputs and film properties as outputs, methods developed within control theory could be used to design closed-loop controllers and to compute optimal input trajectories. However, a major challenge in applying the methods of control theory to a thin film deposition process has been the formulation of models compatible with established control techniques. We consider a lattice model of thin film deposition, which is the basis for stochastic, atomic-scale Monte Carlo simulations of film growth. Instead of analyzing these rule-based dynamics, we focus on the underlying probabilistic “master equation,” a high-order ordinary differential equation. A comparison is made between the film properties obtainable with constant process parameters and with parameters that are periodic in time. In the limit when the input is fast, new constant “effective'” inputs are created that enable film properties unattainable with constant process parameters. The effect of periodic process parameters is also investigated in experiment for a molecular beam epitaxy growth process; initial data will be presented.

**Temporal Patterns in Control**

P. S. Krishnaprasad

Department of Electrical and Computer Engineering

Institute for Systems Research

University of Maryland

In this informal talk we revisit some recurrent themes in control theory. In systems with few controls and many state variables, one common mechanism for steering it to set up temporal patterns in the control signals. Nonlinear control theory "explains" this in the language of Lie brackets, averaging, geometric phases and such. Apparently, in biological locomotion, the relevant principles have come to life over many millions of years with remarkable consistency. However, our understanding of the subtle interplay of mechanics and control for efficient exploitation of temporal patterns is more recent. We suggest that both the lamprey and the roller racer have much to teach us in this regard.

## 1998

**Merging of IC Fabrication and Traditional Manufacturing Methodologies**

Marc Madou

Ohio State University

We present a comparative study of the different precision engineering tools available today, including ultra precision diamond machining, a variety of electrochemical machining techniques, electro-discharge machining (EDM), ion beam milling, laser and e-beam machining, ultrasonic machining, bulk and surface Si micromachining and LIGA. The test-case for applying these different tools will be microfluidic devices and biomedical sensors. Besides the comparison of available tools, appreciation for the differences between absolute and relative manufacturing tolerances, importance of scaling laws and the exploitation of discontinuities of macro-law is emphasized. Guidelines and engineering rules to ease the decision making of when and which micromachining techniques to apply to deliver microparts in an energy efficient way at low cost are introduced. It is the intent of this lecture to arm the audience with a basic approach on how to choose the micromachining tools applicable to the micro-engineering task at hand. One conclusion will be that in the near future traditional and IC manufacturing will merge and that micro-electro-mechanical systems (MEMS) will lead the way in this trend. Another conclusion will be that for biosensors to be cost effective we will have to develop continuous processes such as continuous sputtering and lithography instead of batch processes.

**Development of a GPS based Tracking System for Missile Test & Evaluation**

Larry Levy

Johns Hopkins University Applied Physics Laboratory

Test and evaluation is necessary to determine the effectiveness model of the missile system for high confidence performance prediction, enabling optimal utilization of system assets. A missile tracking system, using Global Positioning System(GPS) satellites, was developed to provide precision trajectory measurements over most of the missile test flight to extract the maximum performance information from each test. The tracking system consisted of a translator in the missile relaying GPS wide band signals to surface receiving stations for digital recording. The recordings were later processed to extract precision range and Doppler, correct for known errors, and combined with missile guidance telemetry in a large (up to 450 states) Kalman filter to estimate the trajectory and the many underlying error sources (up to 100). This yielded a detailed evaluation of all the performance contributors for that test. These estimates were periodically combined with other test flights in a system identification algorithm to determine the statistical performance model of the missile system. The presentation will summarize the development of the tracking and evaluation system, emphasizing the practical problems and design issues encountered.

**Stability and Convergence of Stochastic Approximation Algorithms by the O.D.E. Method**

Vivek S. Borkar

Indian Institute of Science, Department of Computer Science and Automation

This talk will describe recent work (joint, with Sean Meyn) on establishing the stability and convergence of a class of stochastic approximation algorithms by analyzing the O.D.E. limits obtained after suitable rescaling. Applications to some algorithms arising in neurodynamic programming will also be described.

**Nonholonomic Visual Servoing**

Dimitris P. Tsakiris

INRIA, Sophia-Antipolis

Visual servoing is a class of sensor-based control strategies, which have been successfully used for manipulator arms equipped with vision sensors. We are interested in extending these strategies to nonholonomic mobile manipulators, namely mobile robots carrying a hand-eye system and subject to nonholonomic motion constraints. We are also interested in studying the effect that mobility restrictions have on the tasks that an active observer is able to accomplish. In particular, we consider the vision-based stabilization of a mobile manipulator to a desired pose with respect to a target of interest. Instances of this problem occur in practice during docking and parallel parking maneuvers of these vehicles. Our approach involves the use of continuous time-varying state feedback control laws to stabilize the nonholonomic mobile base to its desired pose. The state feedback uses visual data obtained from the camera mounted on the manipulator arm, which tracks continuously the target as the base moves. The experimental evaluation of the proposed techniques employs a mobile manipulator prototype developed in our laboratory and dedicated multiprocessor real-time image processing and control systems.

**Averaging Second-Order Control Systems: Spatial Invariance**

John Baillieul

Boston University

In the mechanics of fluids, structures, and mechanisms, it is well-known that the relative importance of various physical effects change as characteristic length scales are reduced (e.g. friction forces become more important and inertial forces become less important). The guiding principles for controlling mechatronic systems using very small-scale actuators and sensors also change. Motion control for small-scale devices in which control forces are produced by magnetostrictive, electrostrictive, or electrostatic effects involve transduction and rectification of oscillatory signals. Vibrating beams, plates, and membranes as well as electrostatic comb motors have been incorporated in a wide variety of devices, but connections with recent work in the nonlinear control theory of systems with oscillatory inputs have remained unexplored. We summarize recent developments in the control of mechanical systems with oscillatory inputs and pay particular attention to how these results depend on length scales. The talk will be illustrated by videos of recent laboratory experiments, and we shall briefly discuss the B.U. micropendulum experiment.

**U.S. Navy Micro Air Vehicle Development**

Richard J. Foch

Naval Research Laboratory

The U. S. Navy is developing autonomous, electric powered Micro Air Vehicles for military missions. The goal of this program is to develop a small flying vehicle for suppression of enemy air defense. It would have a wingspan of 15 to 20 centimeters and carry a 15 gram payload. Primary research areas include computational and experimental low Reynolds number aerodynamics, a novel navigation scheme, the development of custom electric motors, and the development of the radar jammer payload. Wind tunnel tests of two-dimensional and very low aspect ratio, three-dimensional wings are being performed for Reynolds numbers between 20,000 and 200,000. Waypoint navigation is being pursued as the primary navigation, with an optical flow sensor for collision avoidance. Flight control rules are being optimized using a machine learning program coupled to a six-degree-of-freedom flight simulator. This program is entering its third of five years, and will culminate in a system demonstration at the end of fiscal year 2001.

**Nonlinear Optical Systems with 2D Feedback: Pattern Formation, Phase Distortion Suppression and Image Processing**

Mikhail Vorontsov

Army Research Laboratory

In optical systems with Kerr-type nonlinearity and 2D diffractive feedback, such different dynamic regimes as phase distortion suppression leading to high resolution adaptive wavefront distortion suppression, and spatio-temporal instabilities resulting in pattern and travelling waves formation, and generation of optical turbulence have been recently observed.

Here we discuss the following aspects of nonlinear 2D feedback system spatial dynamics:

1. Basic models of nonlinear 2D feedback systems.

2. Mathematical models: instability balloons, amplitude equations.

3. Spatial filtering in a 2D feedback loop: zero, one and two balloon mode configurations.

4. High resolution phase distortion suppression using 2D feedback systems.

5. Photorefractive amplifier with 2D feedback: signal amplification with optical noise suppression, patterns and travelling waves.

6. Long-range transversal interactions and related patterns.

7. Two-component 2D feedback systems: optical models of nonlinear reaction diffusion type systems.

8. Multiballoon mode coupling: second spatial harmonic generation, coupled hexagons, lattice, interlace, and more.

9. Optical patterns and image recognition.

**MEMS Arrays for Fluidic and Optical Control**

Thomas G. Bifano

Aerospace and Mechanical Engineering

Boston University

Two new types of silicon MEMS arrays for micro-fluidic control and for micro-optical control are described. The fluidic device consists of parallel arrays of electrostatically actuated, bistable mechanical micro-valves for precision control of flow. These devices will find end uses in process control of pressure and flow rate, biomedical dosing, fluidic mixing, active micro-cooling (e.g. for electronic chips), and other flow control applications. The micro valves and micro-pumps described provide basic building blocks for fluidic MEMS devices such as micro-turbine power systems, lightweight, user worn biological and chemical analysis systems, micro-cooling and mixing systems, and micro-chemical processing systems. The optical device is a silicon deformable mirror, capable of correcting time varying aberrations in imaging or beam forming applications. Each mirror is composed of a flexible silicon membrane supported by an underlying array of electrostatic parallel plate actuators. Several deformable mirrors are characterized for their electromechanical performance. Real-time correction of optical aberrations is demonstrated using a single mirror segment connected to a closed loop feedback control system. Control of optical phase with a 100 actuator mirror is described.

**A Behavioral Approach to H_infinity Control**

Jan C. Willems

University of Groningen, Netherlands

The purpose of this talk is to outline an approach to the synthesis of controllers and filters in the behavioral framework. The main advantage is that the results obtained this way are representation independent with all the algorithmic advantages that this entails. The aim is to explain the solution of a problem, but before doing so, a number of background concepts will be introduced.

**Some new results related to two contributions of G.I. Taylor: (i) swimming micro-organisms and (ii) hydrodynamic dispersion**

Howard A. Stone

Division of Engineering and Applied Sciences

Harvard University

What can a fluid dynamicist communicate to an audience in a Control and Dynamical Systems Seminar? Two themes suggest themselves owing to the generic structure of the mathematical/physical problems. The first concerns the manner in which small swimmers may deform themselves in order to achieve motion in a viscous fluid (low Reynolds number hydrodynamics). Here we investigate the possible utility of swimming using traveling waves tangent to the surface of a spherically shaped micro-organism. Second, convective-diffusion equations are familiar and have many common applications. Frequently, the average description of these problems leads again to a convective-diffusion equation in which the velocity gradients contribute to a constant effective dispersion coefficient. We outline two model problems that require spatially dependent dispersivities.

**On Minimality and Similarity Invariance and its Relation with Input-Output Notions for Nonlinear Systems**

Jacquelien Scherpen

Delft University of Technology

For linear systems the understanding of the relations between input-output systems, Hankel operators and minimal state-space realizations is well-developed and has turned out to be very important over the last decades. However, for nonlinear systems the relations are far less clear and well-developed. A set of sufficient conditions in terms of controllability and observability functions will be given, under which a given state space realization of a formal power series is minimal. Specifically, it will be shown that positivity of these functions, plus a few technical conditions, implies minimality. In doing so, connections are established between Hamilton-Jacobi type optimal control theory and the well known necessary and sufficient conditions for minimality in terms of Kalman type rank conditions. Furthermore, a definition of a system Hankel operator is developed for causal L2-stable input-output systems. If a generating series representation of the input-output system is given then an explicit representation of the corresponding Hankel operator is possible. If, in addition, an affine state space model is available with certain stability properties then a unique factorization of the Hankel operator can be constructed with direct connections to well known and new nonlinear Gramian extensions. Finally, preliminary results on singular value type of considerations in combination with the Hankel operator will be briefly discussed.

## 1999

**General Input Balancing and Model Reduction for Linear and Nonlinear Systems**

W. Steven Gray

Old Dominion University

Department of Electrical and Computer Engineering

Model reduction for linear state space systems has been investigated by many researchers over the past twenty years. Perhaps the most widely used methods in control applications are those related to the method of balance realizations introduced by Moore. In this context, a sufficient condition for a balanced realization to exist is minimality, i.e., joint controllability and observability, which can be determined independently from the class of admissible inputs. The input class does, however, play a role in the model reduction process. For example, a state may be strongly influenced by an input stimulus at a certain frequency and unaffected otherwise. Hence it could be deleted from the state variable model if this resonant input is never generated by the applied controller. In both the linear and nonlinear cases, various notions of closed-loop balancing exist where the admissible inputs are assumed to be generated by specific controller types (LQG-optimal, H_inf-optimal, etc.). In the nonlinear setting, the input class plays two roles. As in the linear case, it still plays a direct role in the state deletion decision, but it also plays a role in the observability property. In short, the choice of input class is linked to the existence of a balanced nonlinear realization. In the well known method due to Scherpen, the standing assumption is that the nonlinear system is zero-state observable, i.e., the zero-input is a universal input. In this talk, we present a less restrictive notion of nonlinear balancing where observability is required only over the set of finite energy inputs. This idea then leads naturally to a generalized notion of closed-loop balancing.

**Modeling and Control Issues Concerning Smart Materials with Hysteresis**

Ralph C. Smith

North Carolina State University, Raleigh

CRSC, Department of Mathematics

Modeling and control issues concerning certain smart material actuators utilized in nonlinear regimes will be presented. Piezoceramic, electrostrictive and magnetostrictice materials all exhibit various degrees of hysteresis and nonlinear dynamics at high drive levels. The accurate and efficient quantification of these effects and their incorporation in control design are necessary to attain the full capabilities of the materials. Various modeling techniques and their impact on control design will be presented. The performance of the models will be illustrated for magnetostrictive and relaxor ferroelectric actuators. Linear control methods prove ineffective at high drive levels and certain nonlinear control laws and inverse compensation techniques for smart material applications will be discussed.

**Stabilization of Strongly Nonlinear Systems with Incomplete Model Information **

Kristi Morgansen

Division of Engineering & Applied Sciences

Harvard University

We take the approach of representing a given unknown nonlinear system as the cascade of a linear time invariant system, a nonholonomic integrator of the appropriate dimension, and a second linear time invariant system. In the case where the linear systems are matrix transformations on the state and control spaces, we identify the system parameters by using a method of regression on the system inputs and the projected areas defined by the inputs. If either of the linear systems contain integrators, the resulting cascade will be second order. The placement of integrators relative to the nonholonomic integrator strongly affects the qualitative properties of the resulting system and consequently the structure of the control methods used. In either of these situations, our main interest is to extend the idea of an approximate inverse to this setting. It has previously been shown that the approximate inverse provides a conceptually clear way to approach tracking and stabilization problems associated with the nonholonomic integrator. The work presented shows that the approximate inverse retains its usefulness in the more complex situations encountered here. As a concrete demonstration of the ideas discussed, we present stabilization and tracking results for the well known``ball-plate'' system when we do not have complete information for the system model parameters.

**Motion Control with Limited Communication**

Dimitris Hristu

Division of Engineering & Applied Sciences

Harvard University

Control and communication issues are traditionally decoupled in discussions of decision and control problems because this simplifies the analysis and generally works well for classical models. This fundamental assumption deserves re-examination as control applications spread into areas where lack of time on a network shared by sensors, actuators and the controller is as important as lack of computational power. Such areas include the coordinated control of robots, aerial vehicles (UAVs), MEMS devices and other settings, where many systems must share the attention of a decision-maker. An example of such a system is the HRL planar manipulator. The manipulator includes 2-DOF fingers, tactile sensors and a visual tracking system, all controlled from a centralized computer. Because the communication bus connecting the controller to the manipulator has limited capacity, communication with the controller occurs at discrete times and the controller must choose which actuators/sensors to update/read at a particular time.

These constraints lead to the need for a theory of sampled-data systems where communication and control are intrinsically coupled. In this talk, I will outline such a theory and use it to solve tracking and stabilization problems as well as to quantify "attention" in the context of control systems with limited communication. I will discuss applications of the theory to trajectory tracking problems involving the HRL manipulator and present results showing typical performance improvements that can be achieved in manipulation experiments.

**Characterization, Design, and Modeling of Magnetostrictive Transducers**

Alison B. Flatau

Program Director, Dynamic Systems and Control Program

National Science Foundation

This presentation provides an overview of work on characterization, design, and modeling of magnetostrictive transducers being done in the Aerospace Engineering and Engineering Mechanics Department of Iowa State University. Results from experimental studies are shown examining the broad range of performance achievable through control of transducer operating conditions such as prestress, DC magnetic bias, AC field level, and frequency. Results include studies demonstrating the use of the large delta E effect found in Terfenol-D for control of a tuned vibration absorber, variability of hysteresis and efficiency characteristics with operating conditions and a recent investigation of the elastic modulus and blocked force characterisitics of one of our transducers. Results from an energy-based modeling approach incorporating both the active (magnetostrictive) and passive (elastic) dynamics of our transducer wil also be shown, illustrating the potential this approach has for modeling the nonlinear and hysteretic output typical of magnetostrictive devices.

**Scale Independent Hysteresis Switching and Some of Its Applications**

A. Steven Morse

Center for Computational Vision and Control

Department of Electrical Engineering

Yale University

“Scale-independence'” is a property of certain switching algorithms used in an adaptive context which is key to proving an algorithm's correctness when operating in the face of noise and disturbance inputs. The concept of dwell-time switching, exploited in our earlier work on supervisory control, has the advantage of being scale-independent. Unfortunately, the existence of a prescribed dwell-time makes it impossible to rule out the possibility of finite escape in applications of dwell-time switching to the adaptive control on nonlinear systems. On the other hand, the popular idea of hysteresis switching, originally devised by Middleton, Goodwin, Hill and Mayne, does not have the shortcoming. Unfortunately, hysteresis switching is not a scale-independent algorithm. Moreover, to date it is not known how to analyze systems employing hysteresis switching except in highly unrealistic [noise free, exact matching] situations when switching necessarily in finite time. In this talk we describe, analyze, and compare with dwell-time and hysteresis switching, a new form of chatter-free switching which does not employ a prescribed dwell-time and which is scale independent. To demonstrate the switching logic's utility, we consider its use as a component of an estimator-based supervisor whose purpose is to orchestrate the switching of a sequence of candidate set-point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a siso linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the set-point tracking problems, were the process's transfer function to be one of the members of the subclass. It is shown that if the number of candidate controllers is finite, it is possible to derive in a straight forward manner a reasonably explicit formula for the exponentially weighted L2 gain induced between the supervisory control system's disturbance input and its output tracking error.

**Long-Duration Carrier-Smoothed-Code Algorithm for GPS Positioning**

Li-Sheng Wang

Institute of Applied Mechanics

National Taiwan University

GPS (Global Positioning System) has been extensively used in recent years for surveying, navigation, time transfer, etc. In order to get a centimeter level accuracy positioning, the carrier phase observables must be adopted, along with differential techniques. However, the use of carrier phase alone may require a long convergence period of intialization, and is thus subject to serious problems caused by cycle slip, if used in real-time. On the other hand, algorithms based on pseudo-ranges (or code) can provide less accurate position data once the signal is tracked. To overcome the cycle slip problem, and still be accurate most of the time, the Carrier-Smoothed-Code (CDC) algorithm was developed to synthesize the carrier phase observables and the pseudo-range observables. However, for long-duration positioning, in which problems caused by cycle slip, satellite changes, frequently arise, the CSC algorithm may exhibit positioning jumps. It is desirable to alleviate these jumps to yield a better positioning algorithm. In this talk, an improved scheme, called the Long Duration CSC (LCSC) algorithm, is introduced. A Kalman filter is used to predict the occurrence of cycle slips and to smooth the carrier-smoothed pseudo-range. A fuzzy scheme is designed to obtain the weightings between the carrier phase and the pseudo-range once the cycle slip happens. A least-square scheme based on the weightings of satellite signals is used to handle the problem of satellite changes. From both static and dynamic experiments, the LCSC algorithm indeed provides more stable positioning data in long term positioning.

**Computation of Space and Spectrum in the Owl's Auditory System **

Terry T. Takahashi

Institute of Neuroscience

University of Oregon

No abstract available.

**Stabilization by the Method of Controlled Lagrangians**

Anthony Bloch

Department of Mathematics

University of Michigan

In this talk, which describes joint work with J. Marsden, N. Leonard and D. Chang, I will describe a method for the stabilization of mechanical systems using controlled Lagrangians. The key idea is that of matching, which involves finding new autonomous Lagrangian (the control Lagrangian) which produces the feedback controlled equations for the original mechanical system. The method is based on the type of Lagrangian used in the Kaluza-Klein theory for describing the motion of particle in a magnetic field. The advantage of the method is that it provides a natural Lyapunov function for analyzing stability. Various examples will be discussed, including spherical pendula and satellites. I also will describe the relationship of this work to that of Krishnaprasad, Hamburg, Auckley and others.

**Bursts**

Edgar Knobloch

Physics Department

University of California, Berkeley

In this talk, I will review several mechanisms believed to explain the origin of bursting behavior in different physical systems. I will also describe a new mechanism that generates bursts close to the threshold of an oscillatory instability in systems with symmetry. The mechanism relies on the interaction between nearly degenerate modes brought about via forced symmetry breaking. After describing the properties of the resulting bursts I will discuss several experiments in which such bursts have been observed.

**Learning algorithms for MDPs: recent results**

Vivek S. Borkar

School of Technology and Computer Science

Tata Institute of Fundamental Research, Bombay

No abstract available.

**Riddled Basins of Attraction of Chaotic Systems: Inevitable uncertainties in the outcomes of experiments**

Edward Ott

Department of Electrical and Computer Engineering

University of Maryland

In certain situations, it is possible for the dynamical behavior of chaotic systems to be such that even the qualitative character of the eventual long time motion (i.e., the attractor) may be uncertain. In particular, it is possible that for every initial condition yielding a given type of behavior there exist arbitrarily small perturbation from that initial condition that can yield a qualitatively different behavior. Thus the repeatability of even qualitative outcomes of experiments for such systems comes into question. This phenomenon is due to a "riddled" basin of attraction. (A basin of attraction is the set of initial conditions in state space that yield a particular long time motion). This talk will discuss riddle basins in elementary terms, and will give illustrative numerical and analytical examples.

**Chaotic Laser Dynamics: Control and Noise**

Rajarshi Roy

Department of Physics

University of Maryland

Lasers can display qualitatively different types of chaotic dynamics for certain parameter regimes of operation. Simple control techniques have been applied to chaotic lasers with some success for specific types of dynamics. For other types of dynamics, a given control strategy may fall.

One may characterize the experimentally observed dynamics through time series analysis. The computation of the percentage of "false nearest neighors" gives a measure of the dimensionality of the dynamics. The Lyapunov spectrum is also computed from the experimental time series and compared with the results of numerical models. An important problem is to determine the influence of noise on the chaotic dynamics of the laser.

## 1996

**Geometry and Nonlinear Control, 300 Years After Johann Bernoulli's Brachistochrone Problem**

Hector J. Sussmann

Rutgers University

In 1696, Johann Bernoulli challenged the mathematical community by proposing the "brachistochrone problem". This event is often taken to mark the birth of the Calculus of Variations, but Bernoulli's question was in fact the first optimal control problem ever studied. On the 300th anniversary of the birth of optimal control, we illustrate the power of the methods of modern optimal control theory, especially when coupled with differential-geometric ideas and tools, by means of a number of examples, including the brachistochrone problem, as well as more recent problems such as that of the equivalence of a control system to linear one, that of the structure of optimal trajectories, and the Markov-Dubins-Reeds-Shepp problem on shortest paths subject to a curvature constraint.

**Adaptive Behavior in Natural and Artificial Organisms**

Randall D. Beer

Santa Fe Institute and Case Western Reserve University

At some level, the challenges faced by all agents operating in the real world exhibit important similarities. This suggests that the biologist seeking to understand the neural mechanisms of animal behavior and the roboticist interested in the construction and control of versatile and robust autonomous robots might have much to learn from one another. This talk will survey a variety of projects at this interface between biology and engineering, including a series of legged robots whose design and control are based on principles of insect walking. Our most recent robot can negotiate irregular, slatted and compliant surfaces using a variety of local leg reflexes and a distributed gait controller based on coordination mechanisms that have been described in the stick insect. I will also describe the simulated evolution of neural circuits for controlling the behavior of model agents, as well as some preliminary attempts to understand the dynamics of the evolved agent-environment systems. Behaviors that have been evolved so far include chemotaxis, walking, sequential decision-making and learning, and simple visually-guided behavior.

**Control Concepts for the Intervention and Interrogation of Molecular Dynamics**

Herschel Rabitz

Princeton University

The active manipulation of molecular-scale dynamical events has been a long-standing challenge. Recent years have seen the establishment of the key principles of coherent manipulation of such events, especially through the use of optimal control theory. The relevant concepts will be reviewed, leading to the presentation of a unified formulation for the control (intervention) and inversion (interrogation) of molecular dynamical events. Some projections on the future directions of this field will be presented.

**Linking PET Imaging in Humans to a Model of Neural Mechanisms of Grasping**

Michael A. Arbib

University of Southern California

Our concern is with the brain mechanisms of visually directed reaching and grasping. We approach this key example of visuomotor coordination via a novel synthesis of computer modeling of biologically plausible neural networks, monkey neurophysiology, and studies of human brain activity using Positron Emission Tomography (PET). The key to this synthesis is the technique of synthetic PET imaging developed by Arbib, Amanda Bischoff, Andy Fagg, and Scott Grafton. We first present a computational model of the neural mechanism of grasp generation derived in large part from monkey neurophysiological data. The model is called the FARS (Fagg-Arbib-Rizzolatti-Sakata) model since the model was developed by Andrew Fagg and Arbib to address data from the laboratories of Giacomo Rizzolatti (data on premotor cortex) and Hideo Sakata (data on parietal cortex). Synthetic PET imaging is applied to the model to yield a set of predictions for what we expect to observe in a human experiment. We then describe a human PET experiment conducted by Fagg and Grafton that looks at the processing of instruction stimuli in a conditional task, as well as at the relative representation of different grasp programs. By comparing synthetic PET predictions and the new data, we reflect on how the model may be refined in future work.

## 1997

**Random Walking During Quiet Standing**

J.J. Collins

Boston University, Department of Biomedical Engineering

The task of maintaining erect stance involves a complex sensorimotor control system, the output of which can be highly irregular. Even when a healthy individual attempts to stand still, the center of gravity of his or her body and the center of pressure (COP) under his or her feet continually move about in an erratic fashion. In this paper, we describe a new technique, known as stabilogram-diffusion analysis, for analyzing quiet-standing posture data. With this approach, COP trajectories are analyzed as one-dimensional and two dimensional random walks. We describe how the stabilogram-diffusion analysis leads to the extraction of repeatable COP parameters which can be directly related to the steady-state behavior and functional interaction of the neuromuscular mechanisms underlying the maintenance of erect stance. We also discuss how we have used this technique to gain insight into: (a) the effects of visual input on postural control mechanisms and (b) age related changes in postural control mechanisms.

**Active Material Systems and Meso-Scale Actuator Designs**

Gregory P. Carman

MANE Department, University of California at Los Angeles

Active (smart) materials and Micro-Electro-Mechanical Systems (MEMS) are now focal points for a variety of research and development activities due to the exceptional promise these systems offer. For example, researchers report active control flaps applied to the blade of a rotorcraft significantly reduce the vibrational loads imparted to the hub and, active flow control concepts (including MEMS based concepts) delay stall and decrease drag. While these and other studies indicate the potential advantage for structures containing active materials and MEMS components, fundamental issues such as inadequate force, displacement and bandwidths are inhibiting their use in a broad range of applications. To address these concerns my group conducts experimental studies to understand a materials response to combined electro-magneto-thermo- mechanical loading in the context of designing mechanical structures. To extrapolate the discrete experimental data generated during these tests to other loading regimes, we develop novel nonlinear analytical models that incorporate the complex coupling (also domain motion) arising between combined fields. These mathematical tools provide an avenue to circumvent the expensive "make-it-break-it" approach for designing adaptive structures. In this presentation I will provide an overview of the research work being conducted at UCLA on these topics. The presentation will primarily focus on the experimental/ analytical results obtained an ongoing project funded by the Army Research Office. A novel meso-scale actuator device combining piezoelectric materials with MEMS components is being fabricated to produce a large force displacement actuator. The new actuator is intended for use on a rotorcraft system to reduce vibration, minimize blade vortex interactions, and alleviate dynamic stall.

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