Adaptive Fuzzy Fixed-Time Control for Stochastic Nonstrict Nonlinear Systems With Unknown Backlash-Like Hysteresis
研究了随机非严格反馈系统中未知类齿隙滞后的固定时间跟踪控制问题，提出了一种无需构建滞后逆的自适应模糊控制律，实现半全局实际固定时间稳定。
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.