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

Abstract

In this paper, model‐free finite‐horizon 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 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 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 tracking control method.