An ILC scheme for a class of nonlinear continuous-time systems with time-iteration-varying parameters subject to second-order internal model

Abstract

In this paper, a new iterative learning control (ILC) scheme is proposed to deal with unknown time-iteration-varying parameters for a class of nonlinear continuous-time systems. The parametric non-repetitiveness in the iteration domain is described by a second-order internal model, which includes systems with iteration-invariant parameters as a subset. By incorporating the internal model into the parametric learning law, the proposed ILC scheme can handle more generic systems with parametric uncertainties, and includes existing ILC schemes as a special case with the first-order internal model. The conditions under which the new ILC scheme can guarantee learning convergence are delicately explored. Utilizing the information of the previous two iterations and the method of composite energy function (CEF), it is able to derive point-wise convergence along the time axis and asymptotic convergence along the iteration axis. The controller design is further extended to the case for systems with mixed parameters and unknown time-varying input gain. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.