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Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems
Author(s) -
Liang Yanjun,
Li YuanXin,
Hou Zhongsheng
Publication year - 2021
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3285
Subject(s) - nonlinear system , control theory (sociology) , bounded function , adaptive control , lyapunov function , a priori and a posteriori , fuzzy control system , stability (learning theory) , computer science , mathematics , fuzzy logic , control (management) , mathematical analysis , philosophy , epistemology , machine learning , physics , quantum mechanics , artificial intelligence
Summary The article discusses the adaptive fixed‐time control problems for the stochastic pure‐feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well‐defined smooth functions. A novel semi‐global practical fixed‐time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed‐time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed‐time interval. Finally, the raised method is illustrated by two simulation examples.