Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems

In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. Therefore, the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated. Based on the small-gain theorem, a robust fuzzy observer-based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the NPDS. Furthermore, based on the dissipative theory, an Hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of NPDSs. The MATLAB linear matrix inequality toolbox can be employed to efficiently solve the optimal Hinfin fuzzy observer-based control design problem of NPDSs. Finally, a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer-based control method for the perturbative NPDSs.