Adaptive Iterative Learning Control for First-Order Nonlinearly ParameterizedSystems with Fast-Time-Varying Delays

An adaptive iterative learning control scheme is proposed for a class of first-order nonlinearly parameterized systems with unknown fast-time-varying delays. With respect to the uncertainties of the unknown fast-time-varying delays, a novel exponential-type Lyapunov-Krasovskii function is proposed to overcome the difficulty in designing the controller. The controller and adaptive iterative learning law of unknown time-varying parameters are designed by parameterizing the system. The boundedness of all signals and the convergence of tracking errors are proved by constructing an exponential-type Lyapunov-Krasovskii-like composite energy function. The effectiveness of the proposed control algorithms is verified by a simulation example.