H∞ optimal preview tracking control problem with disturbance attenuation

Abstract

AbstractIn this paper, the H∞ optimal preview tracking control problem of continuous‐time linear system with external disturbance is studied, where the reference signal is previewed and its amplitude does not decay. First, an augmented system with error vector, original system state derivative, and internal model state derivative is constructed, which transforms the tracking problem into the H∞ optimal output regulation problem. Second, the H∞ optimal control method is used to design the controller, and the output regulation of the augmented system is achieved by finding the upper bound of the discount factor. Then the optimal controller, including error integral, preview feed‐forward compensation, and internal model compensation, is obtained for the original problem, and meanwhile the sufficient conditions are also provided to guarantee the existence of the controller. Finally, both theoretical and simulation results show that under the proposed controller, the closed‐loop system can achieve asymptotic tracking and has robustness against the disturbance.