Adaptive Repetitive Control for a Class of Uncertain Nonlinear Systems Based on Additive-state-decomposition and Dynamic Surface Technique

Abstract

This paper proposes an adaptive repetitive control (RC) scheme for a class of uncertain nonlinear systems with mismatched disturbances based on additional-state-decomposition and dynamic surface technique. First, the original tracking problem for uncertain nonlinear system is decomposed into two subproblems, which are RC problem for linear time-invariant (LTI) primary system and robust stabilization problem for uncertain nonlinear secondary system with mismatched disturbances. For LTI primary system, modified RC is used to deal with periodic signals. In addition, the time-delay constant of the repetitive controller is corrected in the frequency domain, which further improves the tracking performance. For uncertain nonlinear secondary system, backstepping control is used to deal with mismatched disturbances, and dynamic surface technique is used to avoid “explosion of terms” in backstepping design. Under the designed composite controller, all signals of the closed-loop system are semi-globally bounded and the system output quickly tracks the reference input. Finally, numerical results illustrate the validity and superiorities of the proposed method.