Iterative learning tracking control for second‐order nonlinear hyperbolic impulsive partial differential systems

• Published in: IET control theory & applications Vol. 17; no. 9; pp. 1227 - 1241
• Main Authors: Dai, Xisheng, Wu, Jing, Zhang, Jianxiang, Zhou, Guopeng
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.06.2023; Wiley
• Subjects: Algorithms; Batch processing; Control systems; Energy consumption; Error analysis; iterative learning control; Machine learning; Nonlinear control; Nonlinear systems; Ordinary differential equations; Partial differential equations; System effectiveness; tracking; Tracking control; Tracking errors; Trajectory analysis
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/cth2.12452

This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results. In this paper, iterative learning control is used to realize the accurate tracking of second‐order hyperbolic partial differential systems with impulsive effect. Considering the fixed initial state and the change of the initial state with the number of iterations.