Model-free Reinforcement Learning for ${H_{2}/H_{\infty}}$ Control of Stochastic Discrete-time Systems

Abstract: This paper proposes a reinforcement learning (RL) algorithm for infinite horizon $\rm {H_{2}/H_{\infty}}$ problem in a class of stochastic discrete-time systems, rather than using a set of coupled generalized algebraic Riccati equations (GAREs). The algorithm is able to learn the optimal control policy for the system even when its parameters are unknown. Additionally, the paper explores the effect of detection noise as well as the convergence of the algorithm, and shows that the control policy is admissible after a finite number of iterations. The algorithm is also able to handle multi-objective control problems within stochastic fields. Finally, the algorithm is applied to the F-16 aircraft autopilot with multiplicative noise.