Almost sure exponential stabilization by discretetime stochastic feedback control
Mao, Xuerong (2016) Almost sure exponential stabilization by discretetime stochastic feedback control. IEEE Transactions on Automatic Control, 61 (6). pp. 16191624. ISSN 00189286

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Abstract
Given an unstable linear scalar differential equation x˙ (t) = αx(t) (α > 0), we will show that the discretetime stochastic feedback control σx([t/τ ]τ )dB(t) can stabilize it. That is, we will show that the stochastically controlled system dx(t) = αx(t)dt +σx([t/τ ]τ )dB(t) is almost surely exponentially stable when σ2 > 2α and τ > 0 is sufficiently small, where B(t) is a Brownian motion and [t/τ ] is the integer part of t/τ . We will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control. The reason why we consider the discretetime stochastic feedback control is because that the state of the given system is in fact observed only at discrete times, say 0, τ, 2τ, • • • , for example, where τ > 0 is the duration between two consecutive observations. Accordingly, the stochastic feedback control should be designed based on these discretetime observations, namely the stochastic feedback control should be of the form σx([t/τ ]τ )dB(t). From the point of control cost, it is cheaper if one only needs to observe the state less frequently. It is therefore useful to give a bound on τ from below as larger as better.
Creators(s):  Mao, Xuerong ORCID: https://orcid.org/0000000267689864; 

Item type:  Article 
ID code:  54009 
Notes:  (c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. 
Keywords:  Brownian motion, stochastic differential delay equations, difference equations , stochastic stabilization, discretetime feedback control, Probabilities. Mathematical statistics, Control and Systems Engineering, Computer Science Applications, Electrical and Electronic Engineering 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date deposited:  19 Aug 2015 09:56 
Last modified:  09 Oct 2020 03:30 
Related URLs:  
URI:  https://strathprints.strath.ac.uk/id/eprint/54009 
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