Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

Abstract

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.