Remote Ph.D. Dissertation Defense: Sheng Cheng

Thursday, May 13, 2021
10:00 a.m.
Zoom link: https://umd.zoom.us/j/2109330813?pwd=SVlSeEtaRlVvcWxGcWFYdFN2cXlLdz09
Maria Hoo
301 405 3681
mch@umd.edu

ANNOUNCEMENT: Remote Ph.D. Dissertation Defense


Name: Sheng Cheng

 

Committee: 

Professor Derek A. Paley, Chair/Advisor

Professor John S. Baras,

Professor Andre L. Tits,

Professor Pratap Tokekar,

Professor Nikhil Chopra 


Date & Time: Thursday, May 13th, 2021 at 10:00 am


Zoom link: https://umd.zoom.us/j/2109330813?pwd=SVlSeEtaRlVvcWxGcWFYdFN2cXlLdz09


Title: Estimation and Control of a Distributed Parameter System by a Team of Mobile Sensors and Actuators


Abstract: The recent development of mobile robots has dramatically extended the scenarios where robots can be deployed to complete tasks autonomously. One of the tasks is monitoring and controlling large-scale spatiotemporal processes, e.g., oil spills and forest fires, which are mainly conducted by human operators. These tasks can pose health threats, cause severe environmental issues, and incur substantial financial costs. Autonomous robots can free human operators from danger and complete tasks in a timely and economically efficient manner. In this dissertation, estimation and control of spatiotemporal processes using mobile sensors and actuators are studied. Spatiotemporal processes vary in both space and time, whose dynamics can be characterized by partial differential equations (PDEs). Since the state space of a PDE is infinite-dimensional, a system with PDE dynamics is also known as a distributed parameter system (DPS). The performance of the estimation and control of a DPS can be enhanced (compared to stationary sensors and actuators) due to the additional degree of freedom induced from the mobility of the sensors and actuators. However, the vehicles carrying sensors and actuators usually have limited onboard resources (e.g., fuels and batteries) whose usage requires judicious decisions. Hence, we propose a new optimization framework that addresses the goal of estimation and control of a spatiotemporal process while considering the limited onboard resources.


In the first part of this dissertation, an optimization framework is proposed to control a DPS modeled by a 2D diffusion-advection equation using a team of mobile actuators. The framework simultaneously seeks optimal control of the DPS and optimal guidance of the mobile actuators such that a cost function associated with both the DPS and the mobile actuators is minimized subject to the dynamics of each. We establish conditions for the existence of a solution to the proposed problem. Since computing an optimal solution requires approximation, we also establish the conditions for convergence to the exact optimal solution of the approximate optimal solution. That is, when evaluating these two solutions by the original cost function, the difference becomes arbitrarily small as the approximation gets finer. Two numerical examples demonstrate the performance of the optimal control and guidance obtained from the proposed approach.

In the second part of this dissertation, an optimization framework is proposed to design guidance for a possibly heterogeneous team of multiple mobile sensors to estimate a DPS modeled by a 2D diffusion-advection process. Owing to the abstract linear system representation of the process, we apply the Kalman-Bucy filter for estimation, where the sensors' measurement innovates the estimate through the covariance operator. We propose an optimization problem that minimizes the sum of the trace of the covariance operator of the Kalman-Bucy filter and a generic mobility cost of the mobile sensors, subject to the sensors' motion modeled by linear dynamics. We establish the existence of a solution to this problem. Moreover, we prove convergence to the exact optimal solution of the approximate optimal solution. That is, when evaluating these two solutions using the original cost function, the difference becomes arbitrarily small as the approximation gets finer. To compute the approximate solution, we use Pontryagin's minimum principle after approximating the infinite-dimensional terms originating from the diffusion-advection process.
The approximate solution is applied in simulation to analyze how a single mobile sensor's performance depends on two important parameters: sensor noise variance and mobility penalty. We also illustrate the application of the framework to multiple sensors, particularly the performance of a heterogeneous team of sensors.

In the third part of this dissertation, a framework of cooperative estimation and control of a 2D diffusion process using collocated mobile sensors and actuators is proposed. Guidance and actuation of the actuators are computed from an optimization problem originated from the first part of the dissertation with additional constraints on the maximum speed and maximum actuation of the mobile actuators. Early lumping is applied such that the optimization problem is solved using a nonlinear programming solver. The sensors' measurement is fed to a Kalman filter to estimate state subject to Gaussian state and measurement noise. The estimation is periodically fed to the optimization problem to compute optimal actuation and guidance in a receding horizon manner. Extensive numerical studies have been conducted to analyze and evaluate the performance of the proposed framework with both parameter sweep on the nondimensional parameters of the optimization problem and Monte Carlo simulations of the entire framework. The framework is demonstrated on an outdoor multi-quadrotor testbed at the Fearless Flight Facility of the University of Maryland.

 

Audience: Graduate  Faculty 

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