Adaptive dynamic surface control design for a class of uncertain nonlinear systems using interval type-2 fuzzy systems

Abstract

This work proposes an adaptive dynamics surface control scheme based on the interval type-II fuzzy system for a class of uncertain nonlinear systems. Interval type-II fuzzy system is used to approximate the uncertain dynamics of the system. Then, a systematic methodology is proposed to design the dynamic surface control scheme. The stability of the closed loop system is guaranteed by the Lyapunov theorem and it is shown that all signals of the closed-loop system are uniformly ultimately bounded. Moreover, the tracking error can be made arbitrary small by proper selection of design parameters. The proposed scheme eliminates the “explosion of complexity” problem. Furthermore, it does not require the availability and boundedness of all derivatives of the reference trajectory for controller design. Finally, numerical example is presented to demonstrate the effectiveness and performance of the proposed scheme.