Trajectory tracking control for nonlinear high-order PDE system based on iterative learning method

This paper addresses a trajectory tracking control method based on iterative learning for the nonlinear fourth-order partial differential equation (PDE) system. A noval iterative learning control law is designed that enables the repeatable Kuramoto-Sivashinsky equation system track the desired trajectory. The Poincar'e-Wirtinger inequality and Cauchy-Schwartz inequality are applied to deal with the function problem in this paper. By using the Gronwall-Bellman lemma and integration by parts technique, a Lyapunov function is constructed and an LMI sufficient condition is provided, respectively. The effectiveness of the proposed iterative learning control method is verified through the convergence proof of the closed-loop Kuramoto-Sivashinsky equation system. Finally, the trajectory tracking curve simulation after multiple iterations is provied in this paper.