Adaptive State Feedback Nash Strategies for Linear Quadratic Discrete-Time Games

Abstract

A substantial effort has been devoted to various adaptive techniques of systems. Most of these concepts work in the control domain, where every system only has one controller. Yet, for the multi-controller counterpart — dynamic games, adaptations are usually considered from a perspective of systems, for an example, evolutionary games. In this paper, we propose a new adaptive approach for linear quadratic discrete-time games with scalar inputs and state feedback Nash strategies. We consider the effort of adaptation under a Fictitious Play (FP) framework with learning algorithms derived from conventional adaptive control methods. Convergence to Nash strategies is proved with the condition that there exists a unique state feedback strategy, which implies that the associated coupled discrete-time algebraic Riccati equations (DAREs) have a unique positive semi-definite solution. The requirement of Persistency of Excitation (PE) is satisfied by proper reference signals to be tracked.