Differential Games of Mixed Strategies in a Variational Inference Framework: An Application to the Perimeter Defense Problem

This dissertation formulates a differential game of mixed strategies as an adversarial Variational Inference (VI) problem so that it can be solved through the lenses of inference. To achieve the aforementioned goal, the dissertation extends two existing tools for solving non-adversarial VI problems to the adver- sarial setting where they are used to solve a non-cooperative differential game of mixed strategies. The contributions of this thesis are as follows: a task variable that relates the likelihood of the success variable conditioned on state and control variables of a stochastic control problem to the objective function is a general tool that links control to Bayesian inference; however, to the best of our knowledge, nowhere in the literature can be found a situation in which it was used such that it is dependent 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 are able to extend results that apply in non-adversarial settings to adversarial settings: we extends Stein Variational Model Predictive Control (SV-MPC) to a Min-Max SV-MPC on one hand while we extends the Cross-Entropy optimization method to a Min-Max Cross-Entropy optimization method. Moreover, we demonstrate the approach using robots as players in the perime- ter defense problem in which multiple defenders are tasked to protect a high- value target from a team of intruders.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Electrical and Computer Engineering

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Kilanga, Dan Monga

Advisor dc:contributor.advisor

• Hutchinson, Seth

Committee members dc:contributor.committeemember

• Tsiotras, Panagiotis
• Davenport, Mark
• Boots, Byron
• Hale, Matthew

• Model Predictive Control
• Monte Carlo simulation
• Stochastic Model, Variational Inference
• Cross Entropy.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1853/80066

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/80066