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Title: Variational Inference and Stochastic Optimal Control Duality in a Multi-Robot Systems Adversarial Paradigm: An Application to the Perimeter Defense Problem
Committee:
Dr. Hutchinson, Advisor
Dr. Tsiotras, Chair
Dr. F. Zhang
Abstract: The objective of the proposed research is to formulate a differential game of mixed strategies as a Variational Inference (VI) problem, and to extend two existing tools for solving non-adversarial VI problems to the adversarial setting where they will be used to solve the aforementioned differential game. The technique that relates the likelihood of success of a task variable conditioned on state and control variables to the objective function is a general tool that links control problems over a time horizon to variational inference; however, there has not been a situation in which the technique was used such that the task variable was conditioned on states and controls that are adversarial. By formulating the problem such that the task variable is conditioned on adversarial state and control variables, we can extend results that apply in non-adversarial settings to adversarial settings. Achievement of the objective will occur through the following contributions: (1) extend Stein Variational Model Predictive Control (SV-MPC) to a Min-Max Stein Variational Model Predictive Control (Min-Max SV-MPC). (2) Extend Cross-Entropy Optimization for Optimal Control to a Min-Max Cross-Entropy Optimization for Stochastic Optimal Control. Moreover, we propose to demonstrate the validity of the approaches on the problem of multiple defenders protecting a high-value target from a team of intruders.
