Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays.The linear matrix inequality (LMI) method is employed to design the nonlinear observer.The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain.The learning law of unknown constant parameter is differential-difference-type,and the learning law of unknown time-varying parameter is difference-type.It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized.By constructing a Lyapunov-Krasovskii-like composite energy function (CEF),we prove the boundedness of all closed-loop signals and the convergence of tracking error.A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.