Adaptive iterative learning control for nonlinearly parameterised systems with unknown time-varying delays and input saturations

In this work, an adaptive iterative learning control (AILC) scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time-varying delays and input saturations. By incorporating a saturation function, a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain, which is used to estimate the unknown time-varying system uncertainty. A new time-weighted Lyapunov–Krasovskii-like composite energy function (LKL-CEF) is designed for the convergence analysis where time-weighted inputs, states and estimates of system uncertainty are all considered. Despite the existence of time-varying parametric uncertainties, time-varying delays, input saturations and local Lipschitz nonlinearities, the learning convergence is guaranteed with rigorous mathematical analysis. Simulation results verify the correctness and effectiveness of the proposed method further.