Distributed Proportional-spatial Derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach.
In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.
Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing, China. wangjunwei1984@yahoo.com.cn
Jun-Wei
JW
Wang
Huai-Ning
HN
Wu
Han-Xiong
HX
Li
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D003661:Decision Support Techniques; D005246:Feedback; D017143:Fuzzy Logic; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*