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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lopez Mejia, Victor Gabriel, "Optimal control strategies and reinforcement learning for dynamical multiagent systems in graphical games" (2019). Electrical Engineering Dissertations. 293.
https://mavmatrix.uta.edu/electricaleng_dissertations/293
Comments
Degree granted by The University of Texas at Arlington