Robust policy iteration for the continuous-time stochastic H∞ control problem with unknown dynamics

In this article, we study a continuous-time stochastic H∞ control problem using reinforcement learning (RL) techniques, which can be formulated as solving a stochastic linear-quadratic two-person zero-sum differential game (LQZSG). First, we propose a PI-based RL algorithm that iteratively solves the stochastic game algebraic Riccati equation using collected state and control data, with all system dynamic information unknown. Notably, the algorithm requires data collection only once during the iteration process. We then provide a convergence proof of the RL algorithm and analyze the robustness of the inner and outer loops of the PI algorithm, demonstrating that when the iteration error is within a certain range, the algorithm converges to a small neighborhood of the saddle point of the stochastic LQZSG problem. Finally, we validate the effectiveness of the proposed RL algorithm through two simulation examples.