Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations

Surong You; Liangjian Hu; Jianqiu Lu; Xuerong Mao

doi:10.1109/TAC.2021.3075177

Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations

Surong You, Liangjian Hu, Jianqiu Lu, Xuerong Mao

Mathematics And Statistics

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35 Citations (Scopus)

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Abstract

This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.

Original language	English
Journal	IEEE Transactions on Automatic Control
Early online date	27 Apr 2021
DOIs	https://doi.org/10.1109/TAC.2021.3075177
Publication status	E-pub ahead of print - 27 Apr 2021

Keywords

Brownian motion
Markov chain
stability in distribution
delay feedback control

Access to Document

10.1109/TAC.2021.3075177

You-etal-TAC-2021-Stabilisation-in-distribution-by-delay-feedback-control-for-hybrid-stochastic-differential-equationsAccepted author manuscript, 252 KB

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
Mao, X. (Principal Investigator)
Royal Society
16/03/17 → 15/06/20
Project: Research Fellowship
Long-time dynamics of numerical solutions of stochastic differential equations
Mao, X. (Principal Investigator)
Royal Society
1/10/16 → 30/09/21
Project: Research
Epsrc Doctoral Training Grant
McFarlane, A. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/10/12 → 30/09/16
Project: Research - Studentship

Cite this

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title = "Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations",

abstract = "This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.",

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author = "Surong You and Liangjian Hu and Jianqiu Lu and Xuerong Mao",

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AU - Hu, Liangjian

AU - Lu, Jianqiu

AU - Mao, Xuerong

N1 - © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, 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 component of this work in other works.

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N2 - This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.

AB - This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.

KW - Brownian motion

KW - Markov chain

KW - stability in distribution

KW - delay feedback control

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DO - 10.1109/TAC.2021.3075177

M3 - Article

SN - 0018-9286

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

ER -

Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations

Abstract

Keywords

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Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Epsrc Doctoral Training Grant

Cite this