Adaptive Fuzzy Finite-Time Tracking Control of Stochastic High-Order Nonlinear Systems With a Class of Prescribed Performance

Abstract

This article investigates the adaptive fuzzy finite-time control problem for a class of high-order stochastic nonlinear systems with a class of exponential type prescribed performance function. It is assumed that the nonlinear functions in the controlled plant are unknown, in which fuzzy logic systems (FLSs) are utilized due to the approximation ability of any unknown continuous functions with arbitrary approximation errors. Based on the FLSs and backstepping design technique, a novel adaptive fuzzy tracking control strategy is proposed to guarantee that the closed-loop nonlinear system is semiglobally finite-time stable in probability via Lyapunov stability theory and It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{o}$</tex-math></inline-formula> formula. Compared with existing results, the transformed error signal was regarded as a stochastic variable. In addition, the expressions of the first and second-order partial derivatives of the transformed error signals are given in this article. Finally, a simulation example with different covariance values is given to show the effectiveness of the proposed control strategy.