Adaptive iterative learning control for 2D nonlinear systems with nonrepetitive uncertainties

This paper explores the iterative learning control (ILC) problem for two‐dimensional (2D) multi‐input multi‐output nonlinear parametric systems by taking all nonrepetitive uncertainties of stochastic initial shifts, different tracking tasks and nonuniform trial lengths into consideration. A 2D stochastic variable is defined with Bernoulli stochastic distribution for the first time to handle iteration‐varying trial lengths. The desired output is incorporated into the learning control law as a feedback to compensate the iterative changes of the tracking tasks. An iterative 2D parameter updating law is established using a new defined virtue tracking error to well address the systems uncertainties and varying trial lengths. Consequently, a novel 2D adaptive ILC (2D‐AILC) is presented by incorporating the control law and parameter updating law. The convergence is proved by introducing both the Lyapunov stability principle and the 2D key technique lemma into the repetitive 2D systems even though the dynamic evolution along with two‐dimensional directions makes it more difficult in the mathematic analysis. The simulation study tests the theoretical results: the presented 2D‐AILC scheme can still accomplish a tracking task exactly even though there exist random initial states, nonrepetitive reference trajectories, and iteration‐varying trial lengths.