Online Stackelberg learning solution for non-zero-sum games with infinite horizon cost*

Abstract

In this paper, we consider online integral RL to derive the optimal solution of mixed H2/H∞ problem. In mixed H2/H∞ control, both control input and deterministic disturbance shaped the Stackelberg game. In this model, the dynamic information is incomplete due to the complexity uncertain environment. The multi-players in this system with hierarchical structure is cooperative, moreover, an extra Lagrange multiplier is required to construct the dynamic relationship of leader and follower. The learning algorithm obtain the solutions of coupled Riccati and Hamilton-Jacobi equations online which derives the adaptive control method approximates the optimal cost function and the Stackelberg form equilibrium. The existence of incentive condition also makes the convergence of the estimation to the realistic date. Moreover, the closed-loop dynamical is guaranteed stability by using Lyapunov stability analysis.