Fuzzy guaranteed cost sampled-data control of nonlinear systems coupled with a scalar reaction–diffusion process

Abstract

A fuzzy guaranteed cost sampled-data control problem is addressed in this paper for a class of nonlinear coupled systems of an n-dimensional lumped parameter system modeled by ordinary differential equation (ODE) with a scalar reaction–diffusion process represented by parabolic partial differential equation (PDE). A Takagi–Sugeno (T–S) fuzzy coupled ODE–PDE model is initially proposed to accurately represent the nonlinear coupled ODE–PDE system. Based on the T–S fuzzy coupled ODE–PDE model, a fuzzy sampled-data controller is subsequently developed via the Lyapunov's direct method to not only locally exponentially stabilize the nonlinear coupled system, but also provide an upper bound of the given cost function. Moreover, a suboptimal fuzzy sampled-data control design is also addressed in the sense of minimizing the upper bound of the cost function. The main contribution of this study lies in that a new parameterized linear matrix inequality (LMI) technique is proposed to reduce the conservativeness of the method, and an LMI-based fuzzy suboptimal sampled-data control design is developed for the nonlinear coupled ODE–PDE system based on this parameterized LMI technique. Simulation results on the sampled-data control of hypersonic rocket car are provided to illustrate the effectiveness and merit of the design method.