Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Jun Wei Wang, Yun Feng, Stevan Dubljevic, Hak-Keung Lam

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Abstract

Via the Takagi-Sugeno (T-S) fuzzy model-based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with Cinfty-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed by the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled-data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators.

Original languageEnglish
Pages (from-to)2625-2638
Number of pages14
JournalIEEE Transactions on Fuzzy Systems
Volume32
Issue number5
DOIs
Publication statusPublished - 1 May 2024

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