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

Junhao Hu, Wei Liu, Feiqi Deng, Xuerong Mao

Research output: Contribution to journalArticle

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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 languageEnglish
Number of pages21
JournalSIAM Journal on Control and Optimization
Publication statusAccepted/In press - 27 Dec 2019

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Feedback Control
Feedback control
Stochastic Equations
Stabilization
Differential equations
Differential equation
Control Function
Theorem
Time Delay
Time delay
Upper bound
Numerical Simulation
Computer simulation
Term
Demonstrate
Design

Keywords

  • Brownian motion
  • Markov chain
  • exponential stability
  • delay feedback control

Cite this

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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.",
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Advances in stabilisation of hybrid stochastic differential equations by delay feedback control. / Hu, Junhao; Liu, Wei; Deng, Feiqi; Mao, Xuerong.

In: SIAM Journal on Control and Optimization, 27.12.2019.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Hu, Junhao

AU - Liu, Wei

AU - Deng, Feiqi

AU - Mao, Xuerong

PY - 2019/12/27

Y1 - 2019/12/27

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

M3 - Article

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

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