Adaptive Fast Finite-Time Fuzzy Control of Stochastic Nonlinear Systems

This article focuses on the adaptive fast finite-time tracking control for a class of stochastic nonlinear systems. To begin with, an adequate qualification is provided for the practically fast finite-time stability. Then, based upon this adequate qualification, a new adaptive fuzzy control scheme is presented. Due to the stochastic disturbance, criteria of the existing fast finite-time stability cannot be applied to the analysis of the stability of stochastic nonlinear systems. To solve this issue, based on Lemma 6, an original criterion of the fast finite-time stability is constructed first in Lemma 7 by using the theorem of the integral mean value. Meanwhile, it would have a huge impact on the analysis of the fast finite-time stability for stochastic nonlinear systems. Finally, a simulation example is carried out for evaluating the validity of the main result.