Robust adaptive fuzzy control for a class of nonlinear coupled ODE–beam systems with boundary uncertainty

Abstract

This paper investigates a robust adaptive fuzzy control problem for a class of nonlinear ordinary differential equations (ODEs) coupled with a beam equation subject to boundary uncertainty. A fuzzy control scheme based on the Takagi–Sugeno (T–S) fuzzy model is employed for the nonlinear ODE subsystem with ODE state feedback. For the beam with boundary uncertainty, a robust adaptive fuzzy boundary control scheme is adopted, where a linear controller via boundary measurements is used to stabilize the beam, and a robust adaptive fuzzy compensator is utilized to counteract the boundary uncertainty. The asymptotic stabilization condition is derived for the nonlinear coupled ODE–beam system by means of the Lyapunov's direct method, which is provided in terms of a set of bilinear matrix inequalities (BMIs). Furthermore, a two-step procedure is presented to solve the BMI feasibility problem by the existing linear matrix inequality (LMI) optimization techniques. Finally, a simulation study is conducted on a flexible spacecraft to demonstrate the effectiveness of the proposed method.