Iterative learning control for one-dimensional fourth order distributed parameter systems

• Published in: Science China. Information sciences Vol. 60; no. 1; pp. 173 - 185
• Main Authors: Fu, Qin, Gu, Panpan, Wu, Jianrong
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 2017; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Computer Science; Control algorithms; Control theory; Distributed parameter systems; Information Systems and Communication Service; Machine learning; Mathematical analysis; Partial differential equations; Research Paper; Tracking errors; Wave equations; 一维; 分布参数系统; 四阶; 抛物方程; 控制问题; 波动方程; 空间误差; 迭代学习控制; P-type learning scheme; fourth order parabolic equation; 分布参数系统; iterative learning control; P型学习律; fourth order wave equation; 四阶波方程; distributed parameter systems; 四阶抛物型方程; 迭代学习控制
• ISSN: 1674-733X; 1869-1919
• DOI: 10.1007/s11432-015-1031-6

This paper addresses the problem of iterative learning control algorithm for high order distributed parameter systems in the presence of initial errors. And the considered distributed parameter systems are composed of the one-dimensional fourth order parabolic equations or the one-dimensional fourth order wave equations. According to the characteristics of the systems, iterative learning control laws are proposed for such fourth order distributed parameter systems based on the P-type learning scheme. When the learning scheme is applied to the systems, the output tracking errors on 2L space are bounded, and furthermore, the tracking errors on 2L space can tend to zero along the iteration axis in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.