Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems

This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ul...

Full description

Saved in:
Bibliographic Details
Published in:Actuators 2024-01, Vol.13 (1), p.3
Main Authors: Long, Zhenzhen, Zhou, Wen, Fang, Liandi, Zhu, Daohong
Format: Article
Language:English
Subjects:
adding a power integrator
Amplification
Control systems
Controllers
Equilibrium
Feedback control
fixed-time stability
Gamma function
Nonlinear systems
Simulation methods
Stabilization
State feedback
state feedback control
stochastic nonlinear system
Stochastic systems
Upper bounds
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c361t-e6f681668481c67874b256a09105dc2e2bef8e886671f06fe70bdbb81d61fbff3
container_end_page
container_issue 1
container_start_page 3
container_title Actuators
container_volume 13
creator Long, Zhenzhen
Zhou, Wen
Fang, Liandi
Zhu, Daohong
description This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.
doi_str_mv 10.3390/act13010003
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_a132eeea8be0434ea06960d27c001586</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A780869950</galeid><doaj_id>oai_doaj_org_article_a132eeea8be0434ea06960d27c001586</doaj_id><sourcerecordid>A780869950</sourcerecordid><originalsourceid>FETCH-LOGICAL-c361t-e6f681668481c67874b256a09105dc2e2bef8e886671f06fe70bdbb81d61fbff3</originalsourceid><addsrcrecordid>eNpNkUFLAzEQhRdRsNSe_AMLHmV1sulms8dSrBaKHqrnMJud1JTtpiYR1F9vtCJlDvMY3nt8MFl2yeCG8wZuUUfGgQEAP8lGJdSiAFlWp0f6PJuEsE0OaBiXwEfZfGE_qCue7Y7ydcTW9vYLo3VD7kyO-bzHEH7kOjr9iiFanT-6obcDoc_XnyHSLlxkZwb7QJO_Pc5eFnfP84di9XS_nM9WheaCxYKEEZIJIaeSaVHLetqWlcCEAlWnSypbMpKkFKJmBoShGtqubSXrBDOtMXycLQ-9ncOt2nu7Q_-pHFr1e3B-o9Anwp4UMl4SEcqWYMqnhCAaAV1ZawBWSZG6rg5de-_e3ilEtXXvfkj4qmyYrKBKzMl1c3BtMJXawbjoUafpaGe1G8jYdJ_VEqRomgpS4PoQ0N6F4Mn8YzJQP19SR1_i3xvagiA</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918505361</pqid></control><display><type>article</type><title>Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems</title><source>Publicly Available Content Database</source><creator>Long, Zhenzhen ; Zhou, Wen ; Fang, Liandi ; Zhu, Daohong</creator><creatorcontrib>Long, Zhenzhen ; Zhou, Wen ; Fang, Liandi ; Zhu, Daohong</creatorcontrib><description>This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.</description><identifier>ISSN: 2076-0825</identifier><identifier>EISSN: 2076-0825</identifier><identifier>DOI: 10.3390/act13010003</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>adding a power integrator ; Amplification ; Control systems ; Controllers ; Equilibrium ; Feedback control ; fixed-time stability ; Gamma function ; Nonlinear systems ; Simulation methods ; Stabilization ; State feedback ; state feedback control ; stochastic nonlinear system ; Stochastic systems ; Upper bounds</subject><ispartof>Actuators, 2024-01, Vol.13 (1), p.3</ispartof><rights>COPYRIGHT 2023 MDPI AG</rights><rights>2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c361t-e6f681668481c67874b256a09105dc2e2bef8e886671f06fe70bdbb81d61fbff3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2918505361/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918505361?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25751,27922,27923,37010,44588,74896</link.rule.ids></links><search><creatorcontrib>Long, Zhenzhen</creatorcontrib><creatorcontrib>Zhou, Wen</creatorcontrib><creatorcontrib>Fang, Liandi</creatorcontrib><creatorcontrib>Zhu, Daohong</creatorcontrib><title>Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems</title><title>Actuators</title><description>This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.</description><subject>adding a power integrator</subject><subject>Amplification</subject><subject>Control systems</subject><subject>Controllers</subject><subject>Equilibrium</subject><subject>Feedback control</subject><subject>fixed-time stability</subject><subject>Gamma function</subject><subject>Nonlinear systems</subject><subject>Simulation methods</subject><subject>Stabilization</subject><subject>State feedback</subject><subject>state feedback control</subject><subject>stochastic nonlinear system</subject><subject>Stochastic systems</subject><subject>Upper bounds</subject><issn>2076-0825</issn><issn>2076-0825</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpNkUFLAzEQhRdRsNSe_AMLHmV1sulms8dSrBaKHqrnMJud1JTtpiYR1F9vtCJlDvMY3nt8MFl2yeCG8wZuUUfGgQEAP8lGJdSiAFlWp0f6PJuEsE0OaBiXwEfZfGE_qCue7Y7ydcTW9vYLo3VD7kyO-bzHEH7kOjr9iiFanT-6obcDoc_XnyHSLlxkZwb7QJO_Pc5eFnfP84di9XS_nM9WheaCxYKEEZIJIaeSaVHLetqWlcCEAlWnSypbMpKkFKJmBoShGtqubSXrBDOtMXycLQ-9ncOt2nu7Q_-pHFr1e3B-o9Anwp4UMl4SEcqWYMqnhCAaAV1ZawBWSZG6rg5de-_e3ilEtXXvfkj4qmyYrKBKzMl1c3BtMJXawbjoUafpaGe1G8jYdJ_VEqRomgpS4PoQ0N6F4Mn8YzJQP19SR1_i3xvagiA</recordid><startdate>20240101</startdate><enddate>20240101</enddate><creator>Long, Zhenzhen</creator><creator>Zhou, Wen</creator><creator>Fang, Liandi</creator><creator>Zhu, Daohong</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SP</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>DOA</scope></search><sort><creationdate>20240101</creationdate><title>Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems</title><author>Long, Zhenzhen ; Zhou, Wen ; Fang, Liandi ; Zhu, Daohong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c361t-e6f681668481c67874b256a09105dc2e2bef8e886671f06fe70bdbb81d61fbff3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>adding a power integrator</topic><topic>Amplification</topic><topic>Control systems</topic><topic>Controllers</topic><topic>Equilibrium</topic><topic>Feedback control</topic><topic>fixed-time stability</topic><topic>Gamma function</topic><topic>Nonlinear systems</topic><topic>Simulation methods</topic><topic>Stabilization</topic><topic>State feedback</topic><topic>state feedback control</topic><topic>stochastic nonlinear system</topic><topic>Stochastic systems</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Long, Zhenzhen</creatorcontrib><creatorcontrib>Zhou, Wen</creatorcontrib><creatorcontrib>Fang, Liandi</creatorcontrib><creatorcontrib>Zhu, Daohong</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Electronics &amp; Communications Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Actuators</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Long, Zhenzhen</au><au>Zhou, Wen</au><au>Fang, Liandi</au><au>Zhu, Daohong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems</atitle><jtitle>Actuators</jtitle><date>2024-01-01</date><risdate>2024</risdate><volume>13</volume><issue>1</issue><spage>3</spage><pages>3-</pages><issn>2076-0825</issn><eissn>2076-0825</eissn><abstract>This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/act13010003</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2076-0825
ispartof Actuators, 2024-01, Vol.13 (1), p.3
issn 2076-0825
2076-0825
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_a132eeea8be0434ea06960d27c001586
source Publicly Available Content Database
subjects adding a power integrator
Amplification
Control systems
Controllers
Equilibrium
Feedback control
fixed-time stability
Gamma function
Nonlinear systems
Simulation methods
Stabilization
State feedback
state feedback control
stochastic nonlinear system
Stochastic systems
Upper bounds
title Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T12%3A15%3A13IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Fixed-Time%20Stabilization%20of%20a%20Class%20of%20Stochastic%20Nonlinear%20Systems&rft.jtitle=Actuators&rft.au=Long,%20Zhenzhen&rft.date=2024-01-01&rft.volume=13&rft.issue=1&rft.spage=3&rft.pages=3-&rft.issn=2076-0825&rft.eissn=2076-0825&rft_id=info:doi/10.3390/act13010003&rft_dat=%3Cgale_doaj_%3EA780869950%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c361t-e6f681668481c67874b256a09105dc2e2bef8e886671f06fe70bdbb81d61fbff3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2918505361&rft_id=info:pmid/&rft_galeid=A780869950&rfr_iscdi=true