Data‐based analysis of iterative learning control for MIMO nonaffine nonlinear systems with multiple nonrepetitive uncertainties

Abstract

Two challenging problems are addressed in this work for the convergence analysis of iterative learning control (ILC), that is, the rigorous assumption on repetitive conditions and the severe dependence on linear or nonlinear parametric models. Consequently, a data‐based analysis method of ILC is presented for a general multi‐input multi‐output nonaffine nonlinear system in the existence of multiple nonrepetitive uncertainties in initial states, external disturbances, reference trajectories, and plant models. An extended iterative dynamic relationship is constructed to extract the linear relationship of I/O dynamics for a nonaffine nonlinear system between two different iterations. The data‐based double dynamics analysis method is developed for analyzing that the tracking error is convergent and the I/O sequence is bounded. The tracking error is shown to converge to a finite bound related to nonrepetitive uncertainties and achieve a perfect convergence if nonrepetitive uncertainties are also iteratively convergent to zero. Notably, the presented analysis method merely uses the I/O data without relying on the plant model. Simulations validate the effectiveness of our theoretical results.