Guaranteed cost distributed fuzzy control design for a class of nonlinear first-order hyperbolic PDE systems

Abstract

This paper is concerned with the guaranteed cost distributed fuzzy (GCDF) control design problem for a class of nonlinear distributed parameter systems described by first-order hyperbolic partial differential equations (PDEs). Using the Takagi-Sugeno (T-S) fuzzy PDE modeling method, a T-S fuzzy PDE model is initially proposed to accurately represent the nonlinear PDE system. Based on the resulting T-S fuzzy PDE model, a distributed fuzzy state feedback controller is subsequently developed to asymptotically stabilize the PDE system and provide an upper bound of the quadratic cost function. The outcome of GCDF control problem is formulated as a space-dependent linear matrix inequality (SDLMI) optimization problem. Moreover, a suboptimal GCDF controller design is proposed to minimize the upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality (LMI) optimization techniques are employed to approximately solve the SDLMI optimization problem. Finally, the proposed design method is applied to the distributed control of a nonisothermal plug-flow reactor (PFR).