Iterative Learning Control for Parabolic PDE Systems via Dissipativity Analysis

ABSTRACT This article focuses on the dissipative iterative learning control (ILC) for parabolic partial differential equation (PDE) systems. Firstly, with the aid of dissipativity analysis, the proposed P‐type learning algorithm can achieve the perfect trajectory tracking based on ‐norm along the iteration axis. Then, by employing the Wirtinger‐based inequality, a novel linear matrix inequality (LMI)‐based sufficient condition is manifested for the parabolic PDE systems to satisfy the dissipativity, and a solvability criterion of the LMI is also given. Furthermore, the dissipative ILC for parabolic PDE systems in the irregular case is investigated. Finally, the effectiveness of the proposed method is illustrated and validated via simulation examples.