Iterative learning control for time-delay nonlinear hyperbolic distributed parameter systems

Abstract

In this paper, we study the application of iterative learning control to a class of nonlinear varying time-delay equations. The handled procedure is the distributed parameter system, hyperbolic type. The selected plan is based on PD-type iterative learning control with initial state learning. Initially, we present the equation and the control law utilised. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the error under the proper assumption are found. Also, a detailed convergence analysis is given based on the once-offered lemmas and Gronwall inequality. Finally, we show the usefulness of the method utilising a numerical model. Abbreviations DPS: distributed parameter system; ILC: iterative learning control; PDE:partial differential equation; DPS: partial difference system; PD: proportional derivative