<inline-formula><tex-math>$H_\infty$</tex-math></inline-formula> Fuzzy Control for a Class of Nonlinear Coupled ODE-PDE Systems With Input Constraint

Abstract

This paper deals with the problem of $H_\infty$ fuzzy control design with an input constraint for a class of coupled systems, which consist of an $n$ -dimensional nonlinear subsystem of ordinary differential equations (ODEs) and a scalar linear parabolic subsystem of partial differential equation (PDE) connected in feedback. Initially, the nonlinear coupled system is represented by a Takagi–Sugeno (T–S) fuzzy-coupled ODE-PDE model. Then, based on the fuzzy model and parallel distributed compensation scheme, a fuzzy state feedback control design is developed via Lyapunov's direct method, such that the resulting closed-loop fuzzy-coupled system is exponentially stable, and a prescribed $H_\infty$ performance of disturbance attenuation is satisfied. The existing condition of the proposed $H_\infty$ fuzzy controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude, a suboptimal $H_\infty$ -constrained fuzzy control problem is also addressed, which is formulated as an LMI optimization problem. Finally, the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness.