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

被引:42
|
作者
Song, Gongfei [1 ]
Lu, Zhenyu [2 ]
Zheng, Bo-Chao [1 ]
Mao, Xuerong [3 ]
机构
[1] Nanjing Univ Informat Sci & Technol, Sch Informat & Control, Jiangsu Collaborat Innovat Ctr Atmospher Environm, Nanjing 210044, Jiangsu, Peoples R China
[2] Nanjing Univ Informat Sci & Technol, Sch Elect & Informat Engn, Nanjing 210044, Jiangsu, Peoples R China
[3] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland
基金
中国国家自然科学基金;
关键词
Brownian motion; Markov chain; generalized Ito formula; almost sure exponential stability; stochastic feedback control; STOCHASTIC DIFFERENTIAL-EQUATIONS; LINEAR-SYSTEMS; DESTABILIZATION; STABILITY; OPTIMIZATION; NOISE;
D O I
10.1007/s11432-017-9297-1
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
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 ai(t) = f(x(t)) by a linear discrete-time stochastic feedback control Ax([t/tau]tau)dB/(t) (namely the stochastically controlled system has the form dx(t) = f(x(t))dt + Ax([t/tau]tau)dB/(t), where B(t) is a scalar Brownian, tau > 0, and [t/tau] is the integer part of t/tau. In this paper, we consider a much more general problem. That is, we study the almost sure stabilization of a given unstable hybrid system ai(t) = f(x(t), r(t)) by nonlinear discrete-time stochastic feedback control u(x([t/tau]tau)dB(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/tau]tau))dB(t), where B(t) is a multi-dimensional Brownian motion and r(t) is a Markov chain.
引用
收藏
页数:16
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