Interplay Between Game Theory and Control Theory

TL;DR

This paper explores the relationship between Game Theory and Control Theory, discussing control-based games and game-based control, with novel mathematical techniques and control strategies.

Contribution

It introduces a novel application of Semi Tensor Product of matrices in control-based Boolean networks and discusses H Infinity robust control via dynamic programming.

Findings

Application of Semi Tensor Product in Boolean networks

Analysis of H Infinity robust control methods

Establishment of direct and inverse relationships between the theories

Abstract

An interrelationship between Game Theory and Control Theory is seeked. In this respect two aspects of this relationship are brought up. To establish the direct relationship Control Based Games and to establish the inverse relationship Game Based Control are discussed. In the attempt to establish the direct relationship Control Based Boolean Networks are discussed with the novel technique of application of Semi Tensor Product of matrices in Differential Calculus. For the inverse relationship H Infinity robust optimal control has been discussed with the help of Dynamic Programming and Pontryagin Minimization Principle.