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Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations

Xiaoyue Li, Xuerong Mao, Denis S. Mukama, Chenggui Yuan Orcid Logo

SIAM Journal on Control and Optimization, Volume: 58, Issue: 5, Pages: 2900 - 2926

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1137/20m1312356

Abstract

Since response lags are required by most of physical systems and play a key role in the feedback control, the aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching di...

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Published in: SIAM Journal on Control and Optimization
ISSN: 0363-0129 1095-7138
Published: Society for Industrial & Applied Mathematics (SIAM) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa57822
first_indexed 2021-09-15T09:05:23Z
last_indexed 2021-12-01T04:17:19Z
id cronfa57822
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spelling 2021-11-30T16:01:02.6699801 v2 57822 2021-09-09 Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2021-09-09 MACS Since response lags are required by most of physical systems and play a key role in the feedback control, the aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in $p$th moment and probability one as well as stable in $H_\8$. The main methods are the strong ergodicity theory of Markov chains and asymptotic analysis of stochastic functional differential equations (SFDEs). For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems.The designed control principles are implementable to stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high strength the controlled SDSs will be stable (bounded) while under the weaker control they will be unstable (unbounded) in mean square. The sample and moment Lyapunov exponents are estimated which have close relationship with the time delays. Journal Article SIAM Journal on Control and Optimization 58 5 2900 2926 Society for Industrial & Applied Mathematics (SIAM) 0363-0129 1095-7138 Brownian motion, Markov chain, Stochastic functional differential equations, Exponential stability, Moment boundedness, Lyapunov functional 17 9 2020 2020-09-17 10.1137/20m1312356 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-11-30T16:01:02.6699801 2021-09-09T07:32:47.4470032 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Xiaoyue Li 1 Xuerong Mao 2 Denis S. Mukama 3 Chenggui Yuan 0000-0003-0486-5450 4 57822__20797__e35605bbfa874ddcbe8dae9babcd78f1.pdf DCSDS-RIS.pdf 2021-09-09T07:44:26.5458892 Output 496621 application/pdf Accepted Manuscript true true eng https://creativecommons.org/licenses/by-nc-nd/2.0/
title Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
spellingShingle Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
Chenggui Yuan
title_short Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
title_full Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
title_fullStr Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
title_full_unstemmed Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
title_sort Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Xiaoyue Li
Xuerong Mao
Denis S. Mukama
Chenggui Yuan
format Journal article
container_title SIAM Journal on Control and Optimization
container_volume 58
container_issue 5
container_start_page 2900
publishDate 2020
institution Swansea University
issn 0363-0129
1095-7138
doi_str_mv 10.1137/20m1312356
publisher Society for Industrial & Applied Mathematics (SIAM)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description Since response lags are required by most of physical systems and play a key role in the feedback control, the aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in $p$th moment and probability one as well as stable in $H_\8$. The main methods are the strong ergodicity theory of Markov chains and asymptotic analysis of stochastic functional differential equations (SFDEs). For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems.The designed control principles are implementable to stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high strength the controlled SDSs will be stable (bounded) while under the weaker control they will be unstable (unbounded) in mean square. The sample and moment Lyapunov exponents are estimated which have close relationship with the time delays.
published_date 2020-09-17T02:23:35Z
_version_ 1822004624913072128
score 11.048042

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