Adaptive Iterative Learning Control of Nonlinearly Parameterized Pure Feedback Nonlinear Systems

Abstract

In this work, an adaptive iterative learning control scheme is proposed to deal with nonlinearly parameterized and completely non-affine pure feedback nonlinear systems. The considered systems are assumed to perform the same operation repeatedly under alignment condition. To overcome the design difficulty from non-affine structure of pure feedback system, mean value theorem is exploited to deduce affine appearance of state variables to be used as virtual controls and actual control. The nonlinearly connected parameters are separated from the local Lipschitz continuous nonlinear functions, and then iterative learning laws and adaptive iterative learning laws are designed. Lyapunov functional stability analysis method has been used to prove the stability of the closed-loop control system and the convergence of tracking error to zero as iteration goes to infinity. Simulation results are provided to illustrate the performance of the proposed scheme.