H∞ Fuzzy Control for Nonlinear Fourth-Order Parabolic Equation Subject to Input Delay

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 52; no. 4; pp. 2531 - 2539
• Main Authors: Kang, Wen, Ding, Da-Wei, Guo, Bao-Zhu, Li, Qing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ control; Actuators; Closed loop systems; Delays; Feedback control; Formulas (mathematics); Fuzzy control; Fuzzy model; H-infinity control; Linear matrix inequalities; linear matrix inequalities (LMIs); Mathematical model; Nonlinear control; nonlinear fourth-order parabolic equation; Process control; Sensors
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2021.3049289

This article discusses <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> fuzzy control for the nonlinear fourth-order parabolic equation with input delay via collocated actuator/sensor pairs. We suggest that the interval [0, 1] is divided into <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> subdomains, where sensors provide spatially averaged/point discrete-time state measurements. The control design strategy is proposed based on output measurements. We derive constructive conditions ensuring that the resulting closed-loop system is internally exponentially stable and has <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> performance by means of the Lyapunov approach.