Data-driven nonlinear ILC with varying trial lengths

Abstract

This work considers randomly varying trial lengths of a nonlinear and non-affine repetitive system and proposes a data-driven nonlinear iterative learning control (DDNILC) method via dynamic linearization. A nonlinear learning control law and a nonlinear parameter estimation law are developed by introducing a stochastic variable to describe the varying trial lengths. The learning gain is both nonlinear and iteration-time-varying, and is iteratively estimated through the parameter updating law so that the system uncertainties can be addressed more effectively. Moreover, the results are extended to the MIMO case. The proposed methods as well as the introduced dynamic linearization are data-driven without the need of an explicit model. Under the Bernoulli distribution assumption, the convergence analysis is performed rigorously in the probability sense. Illustrative examples are provided to verify the derived theoretical results.