Advances in stabilisation of hybrid stochastic differential equations by delay feedback control

Junhao Hu; Wei Liu; Feiqi Deng; Xuerong Mao

doi:10.1137/19M1270240

Advances in stabilisation of hybrid stochastic differential equations by delay feedback control

Junhao Hu, Wei Liu, Feiqi Deng, Xuerong Mao

Mathematics And Statistics

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Abstract

A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of HSDEs. Methods to find the upper bound of the length of the time delay are also investigated. Numerical simulations are presented to demonstrate the new theorem.

Original language	English
Pages (from-to)	735–754
Number of pages	20
Journal	SIAM Journal on Control and Optimization
Volume	58
Issue number	2
Early online date	10 Mar 2020
DOIs	https://doi.org/10.1137/19M1270240
Publication status	E-pub ahead of print - 10 Mar 2020

Keywords

Brownian motion
Markov chain
exponential stability
delay feedback control

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10.1137/19M1270240

Hu-etal-SIAM-JOCO-2020-Advances-in-stabilisation-of-hybrid-stochastic-differentialAccepted author manuscript, 501 KB

Cite this

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title = "Advances in stabilisation of hybrid stochastic differential equations by delay feedback control",

abstract = "A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of HSDEs. Methods to find the upper bound of the length of the time delay are also investigated. Numerical simulations are presented to demonstrate the new theorem.",

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AU - Hu, Junhao

AU - Liu, Wei

AU - Deng, Feiqi

AU - Mao, Xuerong

PY - 2020/3/10

Y1 - 2020/3/10

N2 - A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of HSDEs. Methods to find the upper bound of the length of the time delay are also investigated. Numerical simulations are presented to demonstrate the new theorem.

AB - A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of HSDEs. Methods to find the upper bound of the length of the time delay are also investigated. Numerical simulations are presented to demonstrate the new theorem.

KW - Brownian motion

KW - Markov chain

KW - exponential stability

KW - delay feedback control

UR - https://epubs.siam.org/toc/sjcodc/58/1

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DO - 10.1137/19M1270240

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

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Advances in stabilisation of hybrid stochastic differential equations by delay feedback control

Abstract

Keywords

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Other files and links

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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

Cite this

Advances in stabilisation of hybrid stochastic differential equations by delay feedback control

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

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

Cite this