Nonlinear iterative learning by an adaptive Lyapunov technique

Abstract

We consider the iterative learning control problem from an adaptive control viewpoint. It is shown that some standard Lyapunov adaptive designs can be modi ed in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. Some of the common assumptions of nonlinear iterative learning control are relaxed: eg. we relax the common linear growth asssumption on the nonlinearities and handle systems of arbitrary relative degree. It is shown that generally a linear rate of convergence of the MSE can be achieved, and a simple robustness analysis is given. For linear plants we show that a linear rate of MSE convergence can be achieved for non-minimum phase plants.

An adaptive learning controller for MIMO uncertain feedback linearizable nonlinear systems

“…The ALC without input learning is proposed in SISO systems [15,16] and can also control this SISO system (Fig. 4).…”

“…Afterward, the results were extended to a class of nonlinear systems. The state-tracking problems for the parametric uncertain system in the normal form [15] and with time-varying parameters [16] were solved, where parameter adjustment was performed in the time domain [15] and iteration domain [16], respectively. A large class of uncertain nonlinear system was considered in [17,18] using the hybrid system parameter adjustment technique.…”

A survey on iterative learning control for nonlinear systems

“…When the control task repeats over a finite interval [0, T ], adaptive ILC is more suitable. A differential adaptive learning law is (French and Rogers 2000) …”

“…It is proven in French and Rogers (2000) that the control law (24) together with the adaptive learning law (22) and (23) achieves error convergence in L 2 norm. The analysis can be carried out using a Lyapunov-like function…”

Repetitive learning control of nonlinear systems over finite intervals

“…This approach offers various learning laws such as iterative learning [15,16], differential learning [17,18], and differentialiterative learning laws [19]. The dynamics uncertainties are assumed to be able to be parametrized in many published studies.…”