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

In this paper, we propose a new iterative learning control (ILC) scheme, which is devoted to dealing with unknown parameters that are both time varying and iteration varying. In particular, we consider iteration-varying parameters that are generated by a second-order internal model. By incorporating the internal model into the parametric learning law, the ILC scheme can handle more generic nonlinear systems and more generic parametric uncertainties, comparing with existing ILC schemes that are first order in essence. We further explore the conditions under which the new ILC scheme can guarantee learning convergence. Utilizing the information of previous two iterations and the method of composite energy function (CEF), we are able to derive pointwise convergence along the time axis and asymptotic convergence along the iteration axis.