Open AccessStabilization of stochastic functional differential systems by steepest descent feedback controls
Author(s) -
Yang Xuetao,
Zhu Quanxin
Publication year - 2021
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12082
Subject(s) - mathematics , control theory (sociology) , exponential stability , gradient descent , method of steepest descent , operator (biology) , lyapunov function , exponential function , stability (learning theory) , mathematical optimization , mathematical analysis , artificial neural network , computer science , control (management) , nonlinear system , physics , artificial intelligence , biochemistry , chemistry , repressor , quantum mechanics , machine learning , transcription factor , gene
The mean‐square exponential stabilization and stochastically asymptotical stabilization for a class of stochastic functional differential systems is studied. Based on the definitions of derivatives of functionals, the generalized Itô operator for functionals and compound functions is established. Furthermore, the novel Lyapunov functionals and the induced steepest descent feedback controls are constructed to obtain such stability conditions that are weaker than the classical ones. Together with the generalized Itô operator and the steepest descent feedback controls, mean‐square exponential stabilization and stochastically asymptotical stabilization for stochastic functional differential systems are investigated, respectively. As applications, two examples are given to illustrate the derived results: one is a stochastic mass–spring–damper model and the other is a numerical example with simulation figures.