Backstepping based adaptive iterative learning control for non-strict feedback systems with unknown input nonlinearities

Abstract

The initial state inconsistency and iteration-varying trajectory problems are considered in adaptive iterative learning control (AILC) to enhance the tracking performance of the non-strict feedback systems with unknown input nonlinearities. Through constructing an error reference trajectory independence of the reference signal, the restrictions on the initial condition and reference trajectory are both relaxed. Subsequently, a backstepping-based AILC methodology is systematically presented to ensure that the error reference trajectory can be followed by the actual tracking error. Integral Lyapunov functions are employed to design the recursive controllers, avoiding potential singularity problems resulting from the differentiation of gain functions. Rigorous analysis is provided without imposing constraints on the control gain functions to demonstrate tracking error convergence. Numerical simulations are included to illustrate the efficacy of the proposed method.