Hybrid Robust Boundary and Fuzzy Control for Disturbance Attenuation of Nonlinear Coupled ODE-Beam Systems With Application to a Flexible Spacecraft

摘要

This paper introduces a hybrid robust boundary and fuzzy control design for disturbance attenuation of a class of coupled systems described by nonlinear ordinary differential equations (ODEs) and two nonlinear beam equations. Initially, a Takagi–Sugeno (T–S) model is employed to exactly represent the nonlinear ODE subsystem. Then, a fuzzy controller is designed for the ODE subsystem based on the T–S fuzzy model, and a robust boundary controller via beam boundary measurements is proposed for the nonlinear beam subsystem. Such a hybrid robust boundary and fuzzy controller is developed in terms of a set of space-dependent bilinear matrix inequalities (BMIs) by Lyapunov's direct method, which can exponentially stabilize the coupled system in the absence of disturbances and achieve an prescribed performance of disturbance attenuation in the presence of disturbances. Furthermore, in order to make the level of disturbance attenuation as small as possible, a suboptimal control problem is formulated as a BMI optimization problem. A two-step procedure is subsequently presented to solve this BMI optimization problem by the existing linear matrix inequality optimization techniques. Finally, the proposed control method is applied to the control of a flexible spacecraft to illustrate its effectiveness.