Exponential stabilisation of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations

Ran Dong, Xuerong Mao, Stewart A Birrell

Research output: Contribution to journalArticle

2 Downloads (Pure)

Abstract

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, the time-varying observation frequencies have not been considered yet. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodictime-varying frequencies. This paper investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This paper provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p >1 and almost sure exponential stability. The Lyapunov method and inequalities are main tools of our derivation and analysis. The existence of observation interval sequence is verified and one way of its calculation is provided. Finally, an example is given for illustration. Our new techniques not only reduce the observational cost by reducing observation frequency dramatically, but also offer the flexibility on system observation settings. This paper allows readers to set observation frequencies for some time intervals according to their needs to some extent.
Original languageEnglish
Number of pages11
JournalIET Control Theory and Applications
Publication statusAccepted/In press - 2 Jan 2020

Fingerprint

Discrete Time Observations
Exponential Stabilization
Stochastic systems
Periodic Systems
Asymptotic stability
Stochastic Systems
Feedback Control
Feedback control
Continuous Time
Stabilization
Lyapunov methods
Time varying systems
Differential equations
Time-varying
Costs
Almost Sure Exponential Stability
Lyapunov Inequality
Markovian Switching
Interval
Lyapunov Methods

Keywords

  • stochastic differential equations
  • exponential stabilisation
  • Markovian switching
  • periodic stochastic systems
  • feedback control
  • discrete-time observations

Cite this

@article{2a5fae0bc51c449da25c4ce39ca94aed,
title = "Exponential stabilisation of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations",
abstract = "Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, the time-varying observation frequencies have not been considered yet. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodictime-varying frequencies. This paper investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This paper provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p >1 and almost sure exponential stability. The Lyapunov method and inequalities are main tools of our derivation and analysis. The existence of observation interval sequence is verified and one way of its calculation is provided. Finally, an example is given for illustration. Our new techniques not only reduce the observational cost by reducing observation frequency dramatically, but also offer the flexibility on system observation settings. This paper allows readers to set observation frequencies for some time intervals according to their needs to some extent.",
keywords = "stochastic differential equations, exponential stabilisation, Markovian switching, periodic stochastic systems, feedback control, discrete-time observations",
author = "Ran Dong and Xuerong Mao and Birrell, {Stewart A}",
year = "2020",
month = "1",
day = "2",
language = "English",
journal = "IET Control Theory and Applications",
issn = "1751-8644",

}

TY - JOUR

T1 - Exponential stabilisation of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations

AU - Dong, Ran

AU - Mao, Xuerong

AU - Birrell, Stewart A

PY - 2020/1/2

Y1 - 2020/1/2

N2 - Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, the time-varying observation frequencies have not been considered yet. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodictime-varying frequencies. This paper investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This paper provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p >1 and almost sure exponential stability. The Lyapunov method and inequalities are main tools of our derivation and analysis. The existence of observation interval sequence is verified and one way of its calculation is provided. Finally, an example is given for illustration. Our new techniques not only reduce the observational cost by reducing observation frequency dramatically, but also offer the flexibility on system observation settings. This paper allows readers to set observation frequencies for some time intervals according to their needs to some extent.

AB - Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, the time-varying observation frequencies have not been considered yet. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodictime-varying frequencies. This paper investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This paper provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p >1 and almost sure exponential stability. The Lyapunov method and inequalities are main tools of our derivation and analysis. The existence of observation interval sequence is verified and one way of its calculation is provided. Finally, an example is given for illustration. Our new techniques not only reduce the observational cost by reducing observation frequency dramatically, but also offer the flexibility on system observation settings. This paper allows readers to set observation frequencies for some time intervals according to their needs to some extent.

KW - stochastic differential equations

KW - exponential stabilisation

KW - Markovian switching

KW - periodic stochastic systems

KW - feedback control

KW - discrete-time observations

UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4079545

M3 - Article

JO - IET Control Theory and Applications

JF - IET Control Theory and Applications

SN - 1751-8644

ER -