On the Solvability of Feedback Complete Linearization of Nonlinear Stochastic Systems
In this paper, solvability of the feedback complete linearization problem for single input nonlinear stochastic systems with multidimensional plant noise has been studied. Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. The proposed theorem...
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| Veröffentlicht in: | IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2020-03, Vol.50 (3), p.1074-1082 |
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| container_title | IEEE transactions on systems, man, and cybernetics. Systems |
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| creator | Beheshtipour, Zohreh Khaloozadeh, Hamid Amjadifard, Roya |
| description | In this paper, solvability of the feedback complete linearization problem for single input nonlinear stochastic systems with multidimensional plant noise has been studied. Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. The proposed theorem recognizes the existence of the diffeomorphism and feedback law for linearizing the nonlinear stochastic system without finding them. Checking the conditions of the proposed theorem in order to recognize the solvability of the feedback complete linearization problem, needs only simple matrices multiplication instead of complete solving the problem. The previous works need to solve a set of partial differential equations to recognize the solvability of the problem. The nonlinear stochastic systems that satisfy the conditions of the proposed theorem are completely linearizable, then linear stochastic control methods can be applied to control them and more accurate results in less computation will be achieved. Two numerical examples illustrate the theoretical results. |
| doi_str_mv | 10.1109/TSMC.2017.2689774 |
| format | Article |
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Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. The proposed theorem recognizes the existence of the diffeomorphism and feedback law for linearizing the nonlinear stochastic system without finding them. Checking the conditions of the proposed theorem in order to recognize the solvability of the feedback complete linearization problem, needs only simple matrices multiplication instead of complete solving the problem. The previous works need to solve a set of partial differential equations to recognize the solvability of the problem. The nonlinear stochastic systems that satisfy the conditions of the proposed theorem are completely linearizable, then linear stochastic control methods can be applied to control them and more accurate results in less computation will be achieved. Two numerical examples illustrate the theoretical results.</description><identifier>ISSN: 2168-2216</identifier><identifier>EISSN: 2168-2232</identifier><identifier>DOI: 10.1109/TSMC.2017.2689774</identifier><identifier>CODEN: ITSMFE</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Adaptive systems ; Control methods ; Differential geometry ; Ear ; Existence theorems ; Feedback ; feedback complete linearization ; Isomorphism ; Linearization ; Multiplication ; nonlinear stochastic systems ; Nonlinear systems ; Optimal control ; Partial differential equations ; Stochastic processes ; Stochastic systems ; Theorems ; Transforms</subject><ispartof>IEEE transactions on systems, man, and cybernetics. Systems, 2020-03, Vol.50 (3), p.1074-1082</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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Systems</title><addtitle>TSMC</addtitle><description>In this paper, solvability of the feedback complete linearization problem for single input nonlinear stochastic systems with multidimensional plant noise has been studied. Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. The proposed theorem recognizes the existence of the diffeomorphism and feedback law for linearizing the nonlinear stochastic system without finding them. Checking the conditions of the proposed theorem in order to recognize the solvability of the feedback complete linearization problem, needs only simple matrices multiplication instead of complete solving the problem. The previous works need to solve a set of partial differential equations to recognize the solvability of the problem. The nonlinear stochastic systems that satisfy the conditions of the proposed theorem are completely linearizable, then linear stochastic control methods can be applied to control them and more accurate results in less computation will be achieved. Two numerical examples illustrate the theoretical results.</description><subject>Adaptive systems</subject><subject>Control methods</subject><subject>Differential geometry</subject><subject>Ear</subject><subject>Existence theorems</subject><subject>Feedback</subject><subject>feedback complete linearization</subject><subject>Isomorphism</subject><subject>Linearization</subject><subject>Multiplication</subject><subject>nonlinear stochastic systems</subject><subject>Nonlinear systems</subject><subject>Optimal control</subject><subject>Partial differential equations</subject><subject>Stochastic processes</subject><subject>Stochastic systems</subject><subject>Theorems</subject><subject>Transforms</subject><issn>2168-2216</issn><issn>2168-2232</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1LAzEQhoMoWGp_gHhZ8Lw1k-xHcpTFqlDtYdvzkmRnaep2UzepUH-9XVt6mpfheWfgIeQe6BSAyqdl-VFMGYV8yjIh8zy5IiMGmYgZ4-z6kiG7JRPvN5RSYCLjNBuR1aKLwhqj0rU_StvWhkPkmmiGWGtlvqLCbXctBozmtkPV218VrOsG5NN17f8uKoMza-WDNVF58AG3_o7cNKr1ODnPMVnNXpbFWzxfvL4Xz_PYMMlDzGqQFAE0T7jSDCjNc8A8RSO1NAmjqeKAtaEyyZXQSjQpUqrrRiIX0mg-Jo-nu7vefe_Rh2rj9n13fFkxngoJwBN2pOBEmd5532NT7Xq7Vf2hAloNAqtBYDUIrM4Cj52HU8ci4oXPhRQiEfwPgSxsPg</recordid><startdate>20200301</startdate><enddate>20200301</enddate><creator>Beheshtipour, Zohreh</creator><creator>Khaloozadeh, Hamid</creator><creator>Amjadifard, Roya</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-6948-8898</orcidid><orcidid>https://orcid.org/0000-0002-1870-6349</orcidid></search><sort><creationdate>20200301</creationdate><title>On the Solvability of Feedback Complete Linearization of Nonlinear Stochastic Systems</title><author>Beheshtipour, Zohreh ; Khaloozadeh, Hamid ; Amjadifard, Roya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c293t-2d190e11b343ab2100771e75ec9b9c4205a31edc0947a8ba8f5e00bdf9e389cb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Adaptive systems</topic><topic>Control methods</topic><topic>Differential geometry</topic><topic>Ear</topic><topic>Existence theorems</topic><topic>Feedback</topic><topic>feedback complete linearization</topic><topic>Isomorphism</topic><topic>Linearization</topic><topic>Multiplication</topic><topic>nonlinear stochastic systems</topic><topic>Nonlinear systems</topic><topic>Optimal control</topic><topic>Partial differential equations</topic><topic>Stochastic processes</topic><topic>Stochastic systems</topic><topic>Theorems</topic><topic>Transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beheshtipour, Zohreh</creatorcontrib><creatorcontrib>Khaloozadeh, Hamid</creatorcontrib><creatorcontrib>Amjadifard, Roya</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on systems, man, and cybernetics. Systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Beheshtipour, Zohreh</au><au>Khaloozadeh, Hamid</au><au>Amjadifard, Roya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Solvability of Feedback Complete Linearization of Nonlinear Stochastic Systems</atitle><jtitle>IEEE transactions on systems, man, and cybernetics. Systems</jtitle><stitle>TSMC</stitle><date>2020-03-01</date><risdate>2020</risdate><volume>50</volume><issue>3</issue><spage>1074</spage><epage>1082</epage><pages>1074-1082</pages><issn>2168-2216</issn><eissn>2168-2232</eissn><coden>ITSMFE</coden><abstract>In this paper, solvability of the feedback complete linearization problem for single input nonlinear stochastic systems with multidimensional plant noise has been studied. Through a new theorem, necessary and sufficient conditions for the solvability of the problem are provided. 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| subjects | Adaptive systems Control methods Differential geometry Ear Existence theorems Feedback feedback complete linearization Isomorphism Linearization Multiplication nonlinear stochastic systems Nonlinear systems Optimal control Partial differential equations Stochastic processes Stochastic systems Theorems Transforms |
| title | On the Solvability of Feedback Complete Linearization of Nonlinear Stochastic Systems |
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