Adaptive non-cooperative differential games with a regulator

Abstract

This paper considers linear–quadratic non-cooperative non-zero-sum stochastic differential games with a regulator and analyzes the adaptive problem when the systems matrices are unknown to both the regulator and the players. It is a typical problem of game-based control systems(GBCS) introduced and studied recently, which have a hierarchical decision-making structure. The main purpose of the paper is to study how the adaptive strategies can be designed to make the GBCS globally stable and at the same time to ensure a Nash equilibrium reached by both the regulator and the players. Under some suitable conditions on the system matrices, it is shown that the closed-loop adaptive GBCS will be globally stable, and at the same time reach a Nash equilibrium by both the regulator and the players, where the adaptive strategies are constructed based on the least squares estimator, the switching method and the diminishing excitation.