Fuzzy boundary compensator for a semi-linear parabolic PDE system with non-collocated boundary measurement

This paper discusses the problem of exponential stabilization via nonlinear feedback compensator for a semi-linear parabolic distributed parameter system with boundary control and non-collocated boundary observation. In the light of T-S fuzzy partial differential equation (PDE) model and observer-based output feedback control, a fuzzy observer-based output feedback fuzzy compensator is constructed via non-collocated boundary observation such that the resulting closed-loop system is exponentially stable. Both T-S fuzzy control technique and observer-based output feedback control technique are applied to overcome the design difficulties caused by nonlinear system dynamics and non-collocation between control and observation, respectively. By Lyapunov's direct method with a variant of vector-valued weighted Poincaré-Wirtinger inequality, a sufficient condition for the existence of the fuzzy feedback compensator is given in the form of linear matrix inequalities (LMIs). Finally, numerical simulation results are provided to support the proposed feedback control method.