Stabilization and destabilization of hybrid systems by periodic stochastic controls

Xiaoyue  Li; Wei Liu; Xuerong Mao; Junsheng Zhao

doi:10.1016/j.sysconle.2021.104929

Stabilization and destabilization of hybrid systems by periodic stochastic controls

Xiaoyue Li, Wei Liu, Xuerong Mao, Junsheng Zhao

Mathematics And Statistics

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Abstract

This paper aims to determine whether or not a periodic stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system. New methods are developed and sufficient conditions on the stability and instability for hybrid nonlinear systems with periodic stochastic perturbations are provided. These results are then used to examine stabilization and destabilization by periodic stochastic feedback controls, including intermittent stochastic controls.

Original language	English
Article number	104929
Number of pages	10
Journal	Systems and Control Letters
Volume	152
Early online date	21 Apr 2021
DOIs	https://doi.org/10.1016/j.sysconle.2021.104929
Publication status	Published - 30 Jun 2021

Keywords

nonlinear hybrid differential equation
periodic stochastic control
Brownian motion
Markov chain
stationary distribution
stabilization

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10.1016/j.sysconle.2021.104929

Li-etal-SCL-2021-Stabilization-and-destabilization-of-hybrid-systems-by-periodic-stochastic-controlsAccepted author manuscript, 390 KBLicence: CC BY-NC-ND 4.0

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

Cite this

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title = "Stabilization and destabilization of hybrid systems by periodic stochastic controls",

abstract = "This paper aims to determine whether or not a periodic stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system. New methods are developed and sufficient conditions on the stability and instability for hybrid nonlinear systems with periodic stochastic perturbations are provided. These results are then used to examine stabilization and destabilization by periodic stochastic feedback controls, including intermittent stochastic controls.",

keywords = "nonlinear hybrid differential equation, periodic stochastic control, Brownian motion, Markov chain, stationary distribution, stabilization",

author = "Xiaoyue Li and Wei Liu and Xuerong Mao and Junsheng Zhao",

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T1 - Stabilization and destabilization of hybrid systems by periodic stochastic controls

AU - Li, Xiaoyue

AU - Liu, Wei

AU - Mao, Xuerong

AU - Zhao, Junsheng

PY - 2021/6/30

Y1 - 2021/6/30

N2 - This paper aims to determine whether or not a periodic stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system. New methods are developed and sufficient conditions on the stability and instability for hybrid nonlinear systems with periodic stochastic perturbations are provided. These results are then used to examine stabilization and destabilization by periodic stochastic feedback controls, including intermittent stochastic controls.

AB - This paper aims to determine whether or not a periodic stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system. New methods are developed and sufficient conditions on the stability and instability for hybrid nonlinear systems with periodic stochastic perturbations are provided. These results are then used to examine stabilization and destabilization by periodic stochastic feedback controls, including intermittent stochastic controls.

KW - nonlinear hybrid differential equation

KW - periodic stochastic control

KW - Brownian motion

KW - Markov chain

KW - stationary distribution

KW - stabilization

U2 - 10.1016/j.sysconle.2021.104929

DO - 10.1016/j.sysconle.2021.104929

M3 - Article

SN - 0167-6911

VL - 152

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 104929

ER -

Stabilization and destabilization of hybrid systems by periodic stochastic controls

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