Open AccessLyapunov‐based iterative learning feedback control design for parabolic MIMO PDEs with time‐varying delays
Author(s) -
Liu Yaqiang,
Wu Zongze,
Lai Jialun,
Li Jianzhong,
Xie Shengli
Publication year - 2022
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12272
Subject(s) - iterative learning control , control theory (sociology) , piecewise , mathematics , convergence (economics) , mimo , lyapunov function , initial value problem , mathematical optimization , computer science , control (management) , nonlinear system , artificial intelligence , mathematical analysis , beamforming , economic growth , statistics , physics , quantum mechanics , economics
This paper presents an iterative learning control approach to achieve precise tracking control for a class of repeatable parabolic multiple‐input–multiple‐output (MIMO) partial differential equations (PDEs) with time‐varying delays over a finite time interval. Feedback control is utilised in the iterative learning control system to improve the convergence speed of the repeatable system. A Lyapunov–Krasovskii functional is constructed to deal with the time‐varying delay problem caused by the model uncertainty of MIMO PDEs. Collocated piecewise control and piecewise measurement is considered based on the distributions of actuators and sensors to generate multiple inputs and multiple outputs. By using the mean value theorem for integrals, variants of the Poincaré–Wirtinger inequality in the 1D space, Cauchy–Schwartz inequality and Gronwall–Bellman lemma, sufficient conditions that guarantee the convergence of the iterative learning feedback control system are presented. Numerical simulation experiments and comparisons verify the effectiveness and advantages of the proposed method.