Adaptive repetitive control for a class of uncertain nonlinear systems with input delay

An adaptive repetitive control method is presented in this paper for a class of uncertain nonlinear systems with input delay and mismatched disturbances. The original tracking problem of the uncertain nonlinear system is divided into two subproblems: repetitive control problem of a primary linear time-invariant (LTI) system and robust stabilization problem of a secondary nonlinear system with input delay and mismatched disturbances. Repetitive control is used in the primary LTI system to handle the periodic signal, where a slight correction to amount of the time delay of the repetitive controller is introduced, leading to a significant improvement in steady-state tracking performance. Adaptive backstepping control is used in the secondary nonlinear system to deal with structural uncertainties and external disturbances, where an integral term is used to handle the timedelay input, and a first-order linear filter is used to estimate the derivative of the virtual control input. Both the controller design procedure and the stability criteria are provided. Simulation results demonstrate that the proposed control strategy has satisfactory tracking and disturbance-rejection performance.