Robust H∞ Control for Semilinear Parabolic Distributed Parameter Systems With External Disturbances via Mobile Actuators and Sensors

• Published in: IEEE transactions on cybernetics Vol. 53; no. 8; pp. 4880 - 4893
• Main Authors: Liu, Yaqiang, Wang, Jun-Wei, Wu, Zongze, Ren, Zhigang, Xie, Shengli
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Aerospace electronics; Automation; Closed loops; Compensators; Control design; Control theory; Distributed parameter systems; Disturbances; Feedback; H-infinity control; Mathematical models; Mobile actuators and sensors; Noise measurement; robust <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∞ feedback compensator; Robust control; semilinear parabolic distributed parameter systems (DPSs); Sensors; well-posedness
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2022.3150171

This article presents a robust <inline-formula> <tex-math notation="LaTeX">{H_{\infty }} </tex-math></inline-formula> feedback compensator design approach for semilinear parabolic distributed parameter systems (DPSs) with external disturbances via mobile actuators and sensors. An <inline-formula> <tex-math notation="LaTeX">{H_{\infty }} </tex-math></inline-formula> performance constraint is introduced to deal with the external disturbances from the model and measurement noise. Two types of feedback compensators are designed in terms of the collocated and noncollocated mobile actuators and sensors. By the Lyapunov direct technique, some sufficient conditions based on LMI constraints are proposed for the exponential stability under <inline-formula> <tex-math notation="LaTeX">{H_{\infty }} </tex-math></inline-formula> performance constraints in the <inline-formula> <tex-math notation="LaTeX">\mathcal {L}^{2} </tex-math></inline-formula>-norm. Moreover, the open-loop and closed-loop well-posedness of the semilinear DPSs with external disturbances are analyzed via the <inline-formula> <tex-math notation="LaTeX">{C_{0}} </tex-math></inline-formula>-semigroup theory approach. Finally, extensive numerical simulation results for semilinear DPSs with external disturbances via collocated and noncollocated mobile actuators and sensors are shown to verify the effectiveness of the proposed method.