Application of the iterative learning control of a non-linear MIMO wave equation. Issue 4 (March 2022) - Meryem, Hamidaoui; Shao, Cheng
Highlights: The control problem of a non-linear MIMO wave equation is considered. To get the optimal control of the PDE, a repetitive process is used, and the applied method is based on the ILC. Not like almost of the ILC algorithm, the initial condition here also has an iterative learning update law based on the tracking error and the state. The convergence condition is proved using fundamental mathematical properties Two ILC schemes are presented, and a small comparison is given. Abstract: The control of the MIMO system has become increasingly famous. However, most of the literature considers the linear system. This paper considers a non-linear MIMO wave equation. The control method proposed in this paper is the ILC controller with initial conditions unfixed. The chosen schemes in this paper are the PD-type ILC and the D-type ILC. Moreover, we give sufficient conditions to guarantee the methods' convergence. Finally, we present a simulation result on a specific numerical example to prove the effectiveness of the proposed control law with a comparison between both schemes.