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 many standard adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. In particular, we show that many of the common assumptions of nonlinear iterative learning control can be relaxed, eg. we relax the common linear growth assumption on the nonlinearities and handle systems of arbitrary relative degree. Furthermore it is shown that these new ILC designs have the power to solve a new ILC problem: the learning of unseen trajectories (generalization). It is shown that generally a linear rate of convergence of the MSE can be achieved, and some simple robustness analyses are given. For linear plants we show that a linear arte of MSE convergence can be achieved for non-minimum phase plants.

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ORCID for E. Rogers: orcid.org/0000-0003-0179-9398

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