Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

作     者：Gongfei SONG Zhenyu LU Bo-Chao ZHENG Xuerong MAO 

作者机构：Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment TechnologySchool of Information and Control Nanjing University of Information Science and Technology School of Electronic and Information Engineering Nanjing University of Information Science and Technology Department of Mathematics and Statistics University of Strathclyde 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2018年第61卷第7期

页      面：130-145页

核心收录：

学科分类：0810[工学-信息与通信工程] 0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Leverhulme Trust (Grant No. RF-2015-385) Royal Society (Grant No. WM160014, Royal Society Wolfson Research Merit Award) Royal Society and Newton Fund (Grant No. NA160317, Royal Society–Newton Advanced Fellowship) Engineering and Physics Sciences Research Council (Grant No. EP/K503174/1) National Natural Science Foundation of China (Grant Nos. 61503190, 61473334, 61403207) Natural Science Foundation of Jiangsu Province (Grant Nos. BK20150927, BK20131000) Ministry of Education (MOE) of China (Grant No. MS2014DHDX020) for their financial support 

主　　题：Brownian motion Markov chain generalized Itö formula almost sure exponential stability stochastic feedback control 

摘      要：Although the mean square stabilization of hybrid systems by feedback control based on discretetime observations of state and mode has been studied by several authors since 2013, the corresponding almost sure stabilization problem has received little attention. Recently, Mao was the first to study the almost sure stabilization of a given unstable system ˙x(t) = f(x(t)) by a linear discrete-time stochastic feedback control Ax([t/τ ]τ)d B(t)(namely the stochastically controlled system has the form dx(t) = f(x(t))dt +Ax([t/τ ]τ)d B(t)), where B(t) is a scalar Brownian, τ 0, and [t/τ ] is the integer part of t/τ. In this paper, we consider a much more general problem. That is, we study the almost sure stabilization of a given unstable hybrid system ˙x(t) = f(x(t), r(t)) by nonlinear discrete-time stochastic feedback control u(x([t/τ ]τ), r([t/τ ]τ))d B(t)(so the stochastically controlled system is a hybrid stochastic system of the form dx(t) = f(x(t), r(t))dt + u(x([t/τ ]τ), r([t/τ ]τ))d B(t)), where B(t) is a multi-dimensional Brownian motion and r(t) is a Markov chain.