Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations
type: Item
instance of: scholarly article
title: Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations
zbMATH Open document ID: 1467.93323
author: Ran Dong
author: Xuerong Mao
published in: Mathematical Control and Related Fields
publication date: 2021-05-05T00:00:00Z
review text: The authors investigate the stabilization via feedback control based on periodic observations for two types of \(n\)-dimensional stochastic differential systems, \[dx(t)= [f(x(t),t)+ u(x(\delta_t),t)]\,dt+ g(x(t),t)\,dB(t)\] and \[dx(t)= [f(x(t),r(t),t)+ u(x(\delta_t),r(\delta_t),t)]\,dt+ g(x(t),r(t),t)\,dB(t),\] where \(B(t)\) is \(m\)-dimensional Brownian motion, \(r(t)\) a right-continuous Markov chain with a finite state space, \(u\) the control function, and \[\delta_t= \sum^k_{j=1} \tau_j\le t< \sum^{k+1}_{j=1}\tau_j\] with \(0\), \(\tau_1\), \(\tau_1+\tau_2\), \(\tau_1+ \tau_2+\tau_3,\dots\) as time points of observation. Explicitly time-dependent coefficients are assumed to be periodically so. The aim of the control is \(L^p\)-stability of the systems for \(p>1\), almost sure asymptotic stability and \(p\)th moment asymptotic stability for \(p\ge 2\). The existence of the interval sequence \(\{\tau_j\}_{j\ge 0}\) is verified, a way to calculate it provided, and an illustrative example given. It is shown how to significantly reduce the observation frequency and thus the control costs.
reviewed by: Heinrich Hering
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7344169
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: periodic stochastic systems
zbMATH Keywords: Markovian switching
zbMATH Keywords: asymptotic stability
zbMATH Keywords: feedback control
zbMATH Keywords: periodic discrete-time observations
MaRDI profile type: Publication
full work available at URL: mcrf.2020017
OpenAlex ID: W2989850955
Wikidata QID: Q126418936
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DOI: 10.3934/MCRF.2020017
description: scientific article; zbMATH DE number 7344169