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 

机构地区：[1]Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology,School of Information and Control, Nanjing University of Information Science and Technology [2]School of Electronic and Information Engineering, Nanjing University of Information Science and Technology [3]Department of Mathematics and Statistics, University of Strathclyde

出　　处：《Science China(Information Sciences)》2018年第7期105-120,共16页中国科学（信息科学）（英文版）

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

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.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.

关 键 词：Brownian motion Markov chain generalized Ito formula almost sure exponential stability stochastic feedback control 

分 类 号：O231[理学—运筹学与控制论]