Iterative Learning Control for MIMO Nonlinear Systems With Iteration-Varying Trial Lengths Using Modified Composite Energy Function Analysis

Most works dealing with trajectory tracking problems in the iterative learning control (ILC) literature assume an iteration domain that has
identical
trial lengths. This fundamental assumption may not always hold in practical applications. To address iteration-varying trial lengths, a new structure of ILC laws has been presented in this article, based on the newly proposed modified composite energy function (mCEF) analysis. The proposed approach is a feedback control scheme that utilizes tracking errors in the current iteration, so that it can deal with iteration-varying system uncertainties. It is also a unified framework such that the traditional ILC problems with identical trial lengths are shown to be a special case of the more general problem considered in this article. Multi-input–multi-output (MIMO) nonlinear systems are considered, which can be subject to parametric system uncertainties and an unknown control input gain matrix function. We show that in the closed loop analysis, the proposed control scheme can guarantee asymptotic convergence on the full-state tracking error over the iteration domain, in the sense of the
$L^{2}_{T_{k}}$
norm, with
$T_{k}$
being the trial length of the
$k$
th iteration. In the end, a simulation example is shown to illustrate the efficacy of the proposed ILC algorithm.