Design of fuzzy adaptive controller based on H ∞ observer for nonlinear hyperbolic partial differential equation systems

Abstract

This paper study the problem of designing a fuzzy adaptive controller based on H ∞ observer for a class of uncertain nonlinear system modeled by first-order hyperbolic partial differential equation (PDE). The purpose of this paper is to design a new adaptive fuzzy law based on the principle of observer such that the first-order hyperbolic PDE system is exponentially stable with a desired H ∞ performance for disturbance attenuation, while the control constraint is respected. Initially, a Takagi-Sugeno (T-S) hyperbolic PDE model is proposed to represent the nonlinear PDE systems. Then the fuzzy adaptive observer with H ∞ controller is designed through seeking the feasible solutions of existing linear matrix inequality (LMI) optimization techniques, so using adjusting observer parameters, the control effectiveness can be estimated by state observer. For uncertain system, by designing the estimate of state observer, and introduced approximately error compensation, then the requirement of square integrability for optimal approximation error is inessential. Finally, the proposed design method is proved that the controller based on fuzzy adaptive H ∞ observer will stabilize the first-order hyperbolic PDE system.