Command-Filtered Backstepping Repetitive Control for a Class of Uncertain Nonlinear Systems Based on Additive State Decomposition

Abstract

This paper presents a command-filtered backstepping repetitive control (RC) method for a class of uncertain nonlinear systems with multiple disturbances, which is based on additive state decomposition (ASD) technique and active disturbance rejection approach. First, the original nonlinear system is decomposed into a linear time-invariant (LTI) primary system with periodic inputs and a nonlinear secondary system with multiple, aperiodic disturbances. The original nonlinear tracking problem is accordingly decomposed into two subproblems: RC problem for an LTI periodic system and a robust stabilization problem for a nonlinear system. By making using of the known information of the model, a linear extended state observer is constructed to estimate the matched total disturbance together with the system states and then a command-filtered backstepping control law incorporating with the estimate of the equivalent input disturbance is developed for the secondary system that ensures the robust stability and compensates for the effects of the multiple disturbances and residual nonlinearity. Stability criterion for each subsystem is established. Moreover, a particle-swarm-optimization algorithm is adopted to simultaneously optimize the controller parameters of the system. Finally, simulations and comparative experiments demonstrate the validity and superiorities of this method.