ORCID Identifier(s)

0000-0003-3989-4091

Graduation Semester and Year

2019

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering

Department

Electrical Engineering

First Advisor

Frank Lewis

Second Advisor

Yan Wan

Abstract

As the number of autonomous agents increases in industrial and urban areas, the development of formal protocols to analyze their behavior as they interact with each other becomes of central interest in control systems research. Each agent in this setting is interested in completing a specific task with considerations of an optimal performance. Game theory has become one of the most useful tools in multiagent systems analysis due to its rigorous mathematical representation of optimal decision making. The analysis of dynamical systems has been developed in the branch of game theory regarded as differential games. The ser of graphical games consider also limited sensing capabilities among the agents, such that they can only measure the state of their closest neighbors. This dissertation presents the formulation of different solutions for differential graphical games. The proposed solutions represent various scenarios for the interactions of multiagent systems, on which the agents face different conditions in their environments, their goals or their ability to speculate about the behavior of their neighbors. First, Bayesian Games are formulated to describe the case on which an agent is uncertain about the intentions of its neighbors. Conditions for Bayes-Nash equilibrium are provided. Then, Minmax strategies are analyzed for graphical games as an alternative to Nash equilibrium. Stability and robustness properties are thoroughly investigated. We prove that minmax strategies improve the robustness properties of the single-agent LQR controller. As a particular application of the applicability of minmax strategies, Pursuit-evasion Games are then analyzed. In these games, different behaviors are obtained between both multiagent teams by varying the individual performance indices. Finally, Minmax Regret and Projection Strategies are proposed as additional solution concepts that allow the agents to make assumptions about the information available to their neighbors.

Keywords

Differential games, Graphical games, Optimal control, Robust control, Reinforcement learning

Disciplines

Electrical and Computer Engineering | Engineering

Comments

Degree granted by The University of Texas at Arlington

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