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Distributed Fuzzy Control Design of Nonlinear Hyperbolic PDE Systems With Application to Nonisothermal Plug-Flow Reactor

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3 Author(s)
Jun-Wei Wang ; Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing, China ; Huai-Ning Wu ; Han-Xiong Li

This paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first-order hyperbolic partial differential equations (PDEs), where the control actuators are continuously distributed in space. The goal of this paper is to develop a fuzzy state-feedback control design methodology for these systems by employing a combination of PDE theory and concepts from Takagi-Sugeno (T-S) fuzzy control. First, the T-S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear first-order hyperbolic PDE system. Subsequently, based on the T-S fuzzy-PDE model, a Lyapunov technique is used to analyze the closed-loop exponential stability with a given decay rate. Then, a fuzzy state-feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities (SDLMIs) from the resulting stability conditions. Furthermore, utilizing the finite-difference approximation method (with a backward difference for the spatial derivative), a recursive algorithm is presented to solve the SDLMIs via the existing LMI optimization techniques. Finally, the developed design methodology is successfully applied to the control of a nonisothermal plug-flow reactor.

Published in:

IEEE Transactions on Fuzzy Systems  (Volume:19 ,  Issue: 3 )