Event

ANNOUNCEMENT: Ph.D. Research Proposal Exam

Name: Amoolya Tirumalai

Committee:

Professor John S. Baras (Chair)

Professor Eyad H. Abed

Professor Andre Tits

Date/time: Thurs. Jan. 20th 2022 (01/20/2022) 1:00PM to 3:00 PM


Location:  Join Zoom Meeting
https://umd.zoom.us/j/91336523004

Meeting ID: 913 3652 300 


Title: Multi-agent inference, decision-making and control: models, structure and performance evaluation
 

Abstract:

Multi-agent systems appear frequently in biology, sociology, economics, and beyond. They are also becoming more important in systems engineering, robotics, and computer science. The developments in multi-agent systems in these synthetic fields center around designing methods to promote or restrict communication, coordination, and collaboration dynamics. One example is in coordinating UAVs to perform attack or surveillance tasks. There are as many more systems that we could list here as there are external threats to defend against or vulnerabilities in systems to exploit.

This work intends to solve design problems in multi-agent systems by rigorous mathematization of the relevant systems and design specifications into identification problems and optimal control problems. In doing so, we can produce guarantees on system performance.

This proposal focuses on four sets of problems. The first two sets are posed in continuous time, and take advantage of mean-field approaches (infinitely-many agents) in describing very-large systems of agents. The second two sets are posed in discrete time, and focus on obtaining designs for systems with finite numbers of agents.

The approaches for the first two sets of problems make use of partial differential equation (PDE) models, and the associated system identification and (optimal) control theory. In turn, these are based heavily on the long history of the Calculus of Variations and functional analysis.

By using such approaches, we do lose track of dynamics for individual agents. Instead, these methods allow us to perform control on entire collectives, or identify the interactions that shape the collective dynamics. A very relevant question is whether optimal controls or the `best' models designed for the very-large collective dynamics will function as intended on smaller collectives. This is the purpose of using mean-field approaches. In particular for control, mean-field games or mean-field-type control problems allow us to pass between finite-size optimal control problems and infinite dimensional optimal control problems.

There is not a similar framework for system identification problems, but we intend
to produce some initial results by using similar approaches to those used in the control
problems. With respect to this, we have successfully implemented numerical solutions to
mean-field system identification problems for UAV swarms in three spatial dimensions
plus time.

The two discrete-time problems focus on very practical issues in communication and neural network-based machine learning. The goal of these problems is to contribute to a rigorous framework which specifies system designs that are robust and adaptive to variations in agent data. We make use of mathematical optimization and game theoretic methods to formulate our problems, and to identify and construct suitable approximate or local solutions to them.

Such frameworks have been used in communications and networking for several decades, but provable robustness of neural networks is a hotly studied open problem. Mathematical optimization-based approaches to solve the robustness problem have, surprisingly, only caught on relatively recently as control theorists and mathematicians have returned to the field.

We hope in this work to make some meaningful contribution to the problems aforementioned.