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Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems
This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0
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| Published in: | Fractal and fractional 2024-05, Vol.8 (5), p.255 |
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| container_title | Fractal and fractional |
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| creator | Yang, Hongli Si, Xindong Ivanov, Ivan G. |
| description | This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0 |
| doi_str_mv | 10.3390/fractalfract8050255 |
| format | article |
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The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.</description><identifier>ISSN: 2504-3110</identifier><identifier>EISSN: 2504-3110</identifier><identifier>DOI: 10.3390/fractalfract8050255</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Algorithms ; Analysis ; constrained state regulation ; Constraints ; Continuous time systems ; Control systems ; Control theory ; Controllers ; Coordinate transformations ; Decomposition ; descriptor fractional-order system ; Engineering ; Equivalence ; Feedback control ; Invariants ; Laws, regulations and rules ; Nonlinear programming ; positive system ; positively invariant set ; State regulation</subject><ispartof>Fractal and fractional, 2024-05, Vol.8 (5), p.255</ispartof><rights>COPYRIGHT 2024 MDPI AG</rights><rights>2024 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-c307t-fbf8852debc2051a5a94c4c25a044bdb9240a028801c4f7263107d24a914b563</cites><orcidid>0000-0002-9019-072X ; 0000-0002-8259-5241 ; 0000-0001-6628-055X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/3059417256/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/3059417256?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25752,27923,27924,37011,44589,74997</link.rule.ids></links><search><creatorcontrib>Yang, Hongli</creatorcontrib><creatorcontrib>Si, Xindong</creatorcontrib><creatorcontrib>Ivanov, Ivan G.</creatorcontrib><title>Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems</title><title>Fractal and fractional</title><description>This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>constrained state regulation</subject><subject>Constraints</subject><subject>Continuous time systems</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Controllers</subject><subject>Coordinate transformations</subject><subject>Decomposition</subject><subject>descriptor fractional-order system</subject><subject>Engineering</subject><subject>Equivalence</subject><subject>Feedback control</subject><subject>Invariants</subject><subject>Laws, regulations and rules</subject><subject>Nonlinear programming</subject><subject>positive system</subject><subject>positively invariant set</subject><subject>State regulation</subject><issn>2504-3110</issn><issn>2504-3110</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNptkU1r3DAQhk1poSHNL-jFkLPT0ZdlHcMmaQMLCcnexUiWFi22tZHkQ_59ld1Seig6jBjN-7yjmab5TuCGMQU_fEJbcDqFAQRQIT41F1QA7xgh8Pmf-9fmKucDAFCpmAB50ZhNXHJJGBY3tq8Fi2tf3H6dsIS4tM8pmsnNbfTtncs2hWOJqX34cKrPOHVPaXSp3VY1praiSljWuOZuF2bXvr7n4ub8rfniccru6k-8bHYP97vNr2779PNxc7vtLANZOm_8MAg6OmMpCIICFbfcUoHAuRmNohwQ6DAAsdxL2jMCcqQcFeFG9OyyeTxjx4gHfUxhxvSuIwZ9SsS015hKsJPThvTKIFe9koIPhiFRxPdUSj445JRX1vWZdUzxbXW56ENcU_1w1gyE4kTSk-PNuWqPFRoWH-sgbT2jm4ONi_Oh5m-lEhxIz0QVsLPApphzcv5vmwT0xy71f3bJfgNrU5Qe</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Yang, Hongli</creator><creator>Si, Xindong</creator><creator>Ivanov, Ivan G.</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-9019-072X</orcidid><orcidid>https://orcid.org/0000-0002-8259-5241</orcidid><orcidid>https://orcid.org/0000-0001-6628-055X</orcidid></search><sort><creationdate>20240501</creationdate><title>Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems</title><author>Yang, Hongli ; Si, Xindong ; Ivanov, Ivan G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c307t-fbf8852debc2051a5a94c4c25a044bdb9240a028801c4f7263107d24a914b563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Analysis</topic><topic>constrained state regulation</topic><topic>Constraints</topic><topic>Continuous time systems</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Controllers</topic><topic>Coordinate transformations</topic><topic>Decomposition</topic><topic>descriptor fractional-order system</topic><topic>Engineering</topic><topic>Equivalence</topic><topic>Feedback control</topic><topic>Invariants</topic><topic>Laws, regulations and rules</topic><topic>Nonlinear programming</topic><topic>positive system</topic><topic>positively invariant set</topic><topic>State regulation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, Hongli</creatorcontrib><creatorcontrib>Si, Xindong</creatorcontrib><creatorcontrib>Ivanov, Ivan G.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</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>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Fractal and fractional</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Hongli</au><au>Si, Xindong</au><au>Ivanov, Ivan G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems</atitle><jtitle>Fractal and fractional</jtitle><date>2024-05-01</date><risdate>2024</risdate><volume>8</volume><issue>5</issue><spage>255</spage><pages>255-</pages><issn>2504-3110</issn><eissn>2504-3110</eissn><abstract>This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. 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| subjects | Algorithms Analysis constrained state regulation Constraints Continuous time systems Control systems Control theory Controllers Coordinate transformations Decomposition descriptor fractional-order system Engineering Equivalence Feedback control Invariants Laws, regulations and rules Nonlinear programming positive system positively invariant set State regulation |
| title | Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems |
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