Finite-horizon H∞ tracking control for discrete-time linear systems

In this paper, model-free finite-horizon H-infinity tracking control for discrete-time linear systems is studied. By formulating an augmented system consisting of the considered linear system and the command generator system, an augmented time-varying Riccati equation whose solutions can achieve the finite-horizon H-infinity tracking control is derived. Then, a time-varying Q-function which contains the control input and disturbance input is designed. A time-varying Q-function-based method is developed to learn the solutions of the finite-horizon H-infinity tracking control problem without knowing the system model information nor any model identification methods. It is proved that the solutions of the time-varying Q-function-based method converge to the optimal solutions of the augmented time-varying Riccati equation. At last, simulation examples are provided to show the feasibility and advantages of the time-varying Q-function-based method compared to the infinite-horizon Q-learning-based H-infinity tracking control method.