Adaptive Fuzzy Fixed-Time Control for Stochastic Nonstrict Nonlinear Systems With Unknown Backlash-Like Hysteresis
Zhumu Fu, Yueyang Wang, Fazhan Tao, Nan Wang, Yongsheng Dong
Abstract
This article explores the fixed-time tracking control problem for stochastic nonstrict systems with unknown backlash-like hysteresis properties. To this end, a novel criterion of semiglobally practical fixed-time stochastic stability is established and proved. First, a continuous-time dynamic model that can be solved explicitly is constructed to model the discontinuous backlash-like hysteresis nonlinear behavior approximatively. Second, the coupling relationship between stochastic disturbance and hysteresis nonlinearity is analyzed, and the role of the coupling terms is attributed to each subsystem using the inequality expansion and the summation order transformation techniques. Then, based on the above analysis, a memory-free stochastic fixed-time control law without constructing the hysteresis inverse is developed recursively in the framework of backstepping by means of the 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> stochastic differential equation theory and the adaptive fuzzy technique, which can achieve semiglobally practical fixed-time stability of stochastic systems with hysteresis properties and the tracking error can converge to a small neighborhood near the origin. Finally, simulation studies for a numerical simulation example and a cart moving on a plane example are shown to verify the feasibility of the rendered approach.