Open AccessStabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode
Author(s) -
Song Gongfei,
Zheng BoChao,
Luo Qi,
Mao Xuerong
Publication year - 2017
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/iet-cta.2016.0635
Subject(s) - control theory (sociology) , mode (computer interface) , discrete time and continuous time , observable , stochastic differential equation , state (computer science) , differential (mechanical device) , hybrid system , control (management) , computer science , feedback control , exponential function , differential equation , discrete time stochastic process , mathematics , control engineering , continuous time stochastic process , engineering , algorithm , physics , statistics , mathematical analysis , artificial intelligence , aerospace engineering , operating system , quantum mechanics , machine learning
Mao recently initiated the study of the mean‐square exponential stabilisation of continuous‐time hybrid stochastic differential equations (SDEs) by the feedback controls based on the discrete‐time observations of the state . However, the feedback controls still depend on the continuous‐time observations of the mode . Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable that we identify the mode at the discrete times when we make observations for the state. Hence, the feedback control should be designed based on the discrete‐time observations of both state and mode . The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE.