Design of distributed fuzzy controllers with constraint for nonlinear hyperbolic PDE systems

This paper investigates the problem of designing a distributed H ∞ fuzzy controller with constraint for a class of nonlinear spatially distributed processes modeled by first-order hyperbolic partial differential equations (PDEs). The purpose of this paper is to design a distributed fuzzy state feedback controller such that the closed-loop PDE system is exponentially stable with a prescribed H ∞ performance of disturbance attenuation, while the control constraint is respected. Initially, a Takagi–Sugeno (T–S) hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the T–S fuzzy PDE model, a distributed H ∞ fuzzy controller design with constraint is developed in terms of a set of coupled differential/algebraic linear matrix inequalities (D/ALMIs) in space. Furthermore, a suboptimal distributed H ∞ fuzzy controller with constraint is proposed to minimize the level of attenuation. The finite difference method in space and the existing linear matrix inequality (LMI) optimization techniques are employed to approximately solve the suboptimal fuzzy control design problem. Finally, the proposed design method is applied to the distributed control of a nonlinear system described by two coupled first-order hyperbolic PDEs to illustrate its effectiveness.