Learning‐based control for discrete‐time constrained nonzero‐sum games

Abstract

Abstract A generalized policy‐iteration‐based solution to a class of discrete‐time multi‐player non‐zero‐sum games concerning the control constraints was proposed. Based on initial admissible control policies, the iterative value function of each player converges to the optimum approximately, which is structured by the iterative control policies satisfying the Nash equilibrium. Afterwards, the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player. Meanwhile, neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints. Finally, two numerical simulations of the discrete‐time two‐player non‐zero‐sum games for linear and non‐linear systems are shown to illustrate the effectiveness of the proposed scheme.

Keywords

• approximation theory
• discrete time systems
• dynamic programming
• game theory
• iterative methods
• learning (artificial intelligence)