Robust H8 tracking of linear discrete-time systems using Q-learning

This paper deals with a robust H-infinity tracking problem with a discounted factor. A new auxiliary system is established in terms of norm-bounded time-varying uncertainties. It is shown that the robust discounted H-infinity tracking problem for the auxiliary system solves the original problem. Then, the new robust discounted H-infinity tracking problem is represented as a well-known zero-sum game problem. Moreover, the robust tracking Bellman equation and the robust tracking Algebraic Riccati equation (RTARE) are inferred. A lower bound of a discounted factor for stability is obtained to assure the stability of the closed-loop system. Based on the auxiliary system, the system is reshaped in a new structure that is applicable to Reinforcement Learning methods. Finally, an online Q-learning algorithm without the knowledge of system matrices is proposed to solve the algebraic Riccati equation associated with the robust discounted H-infinity tracking problem for the auxiliary system. Simulation results are given to verify the effectiveness and merits of the proposed method.