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On controller design for systems on manifolds in Euclidean space
Summary A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space Rn, extend the system from M to the ambient space Rn, and modify it outside M to add transv...
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| Published in: | International journal of robust and nonlinear control 2018-11, Vol.28 (16), p.4981-4998 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c3644-acab2e07b8df1945ca66369c92184aeefe9d6e32daec635b8cb4c50fe15db49f3 |
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| cites | cdi_FETCH-LOGICAL-c3644-acab2e07b8df1945ca66369c92184aeefe9d6e32daec635b8cb4c50fe15db49f3 |
| container_end_page | 4998 |
| container_issue | 16 |
| container_start_page | 4981 |
| container_title | International journal of robust and nonlinear control |
| container_volume | 28 |
| creator | Chang, Dong Eui |
| description | Summary
A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space
Rn, extend the system from M to the ambient space
Rn, and modify it outside M to add transversal stability to M in the final dynamics in
Rn. Controllers are designed for the final system in the ambient space
Rn. Then, their restriction to M produces controllers for the original system on M. This method has the merit that only one single global Cartesian coordinate system in the ambient space
Rn is used for controller synthesis, and any controller design method in
Rn, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system. |
| doi_str_mv | 10.1002/rnc.4294 |
| format | article |
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A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space
Rn, extend the system from M to the ambient space
Rn, and modify it outside M to add transversal stability to M in the final dynamics in
Rn. Controllers are designed for the final system in the ambient space
Rn. Then, their restriction to M produces controllers for the original system on M. This method has the merit that only one single global Cartesian coordinate system in the ambient space
Rn is used for controller synthesis, and any controller design method in
Rn, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.</description><identifier>ISSN: 1049-8923</identifier><identifier>EISSN: 1099-1239</identifier><identifier>DOI: 10.1002/rnc.4294</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Cartesian coordinates ; Control stability ; Control systems design ; Controllers ; Coordinates ; Design engineering ; drone ; Dynamic stability ; Embedded systems ; embedding ; Euclidean geometry ; Euclidean space ; manifold ; Manifolds ; quadcopter ; rigid body ; Rigid structures ; Synthesis ; tracking ; Tracking problem</subject><ispartof>International journal of robust and nonlinear control, 2018-11, Vol.28 (16), p.4981-4998</ispartof><rights>2018 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3644-acab2e07b8df1945ca66369c92184aeefe9d6e32daec635b8cb4c50fe15db49f3</citedby><cites>FETCH-LOGICAL-c3644-acab2e07b8df1945ca66369c92184aeefe9d6e32daec635b8cb4c50fe15db49f3</cites><orcidid>0000-0002-6496-4189</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Chang, Dong Eui</creatorcontrib><title>On controller design for systems on manifolds in Euclidean space</title><title>International journal of robust and nonlinear control</title><description>Summary
A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space
Rn, extend the system from M to the ambient space
Rn, and modify it outside M to add transversal stability to M in the final dynamics in
Rn. Controllers are designed for the final system in the ambient space
Rn. Then, their restriction to M produces controllers for the original system on M. This method has the merit that only one single global Cartesian coordinate system in the ambient space
Rn is used for controller synthesis, and any controller design method in
Rn, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.</description><subject>Cartesian coordinates</subject><subject>Control stability</subject><subject>Control systems design</subject><subject>Controllers</subject><subject>Coordinates</subject><subject>Design engineering</subject><subject>drone</subject><subject>Dynamic stability</subject><subject>Embedded systems</subject><subject>embedding</subject><subject>Euclidean geometry</subject><subject>Euclidean space</subject><subject>manifold</subject><subject>Manifolds</subject><subject>quadcopter</subject><subject>rigid body</subject><subject>Rigid structures</subject><subject>Synthesis</subject><subject>tracking</subject><subject>Tracking problem</subject><issn>1049-8923</issn><issn>1099-1239</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp10E1LAzEQBuAgCtYq-BMCXrxszdemm5uy1A8oFkTPIZtMZMs2qckusv_erfXqaQbm4R14EbqmZEEJYXcp2IVgSpygGSVKFZRxdXrYhSoqxfg5ush5S8h0Y2KG7jcB2xj6FLsOEnaQ28-AfUw4j7mHXcYx4J0JrY-dy7gNeDXYrnVgAs57Y-ESnXnTZbj6m3P08bh6r5-L9ebppX5YF5ZLIQpjTcOALJvKeapEaY2UXCqrGK2EAfCgnATOnAEredlUthG2JB5o6RqhPJ-jm2PuPsWvAXKvt3FIYXqpGaWqkmLJ2KRuj8qmmHMCr_ep3Zk0akr0oR899aMP_Uy0ONLvtoPxX6ffXutf_wPL02by</recordid><startdate>20181110</startdate><enddate>20181110</enddate><creator>Chang, Dong Eui</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-6496-4189</orcidid></search><sort><creationdate>20181110</creationdate><title>On controller design for systems on manifolds in Euclidean space</title><author>Chang, Dong Eui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3644-acab2e07b8df1945ca66369c92184aeefe9d6e32daec635b8cb4c50fe15db49f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Cartesian coordinates</topic><topic>Control stability</topic><topic>Control systems design</topic><topic>Controllers</topic><topic>Coordinates</topic><topic>Design engineering</topic><topic>drone</topic><topic>Dynamic stability</topic><topic>Embedded systems</topic><topic>embedding</topic><topic>Euclidean geometry</topic><topic>Euclidean space</topic><topic>manifold</topic><topic>Manifolds</topic><topic>quadcopter</topic><topic>rigid body</topic><topic>Rigid structures</topic><topic>Synthesis</topic><topic>tracking</topic><topic>Tracking problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chang, Dong Eui</creatorcontrib><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>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>International journal of robust and nonlinear control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chang, Dong Eui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On controller design for systems on manifolds in Euclidean space</atitle><jtitle>International journal of robust and nonlinear control</jtitle><date>2018-11-10</date><risdate>2018</risdate><volume>28</volume><issue>16</issue><spage>4981</spage><epage>4998</epage><pages>4981-4998</pages><issn>1049-8923</issn><eissn>1099-1239</eissn><abstract>Summary
A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space
Rn, extend the system from M to the ambient space
Rn, and modify it outside M to add transversal stability to M in the final dynamics in
Rn. Controllers are designed for the final system in the ambient space
Rn. Then, their restriction to M produces controllers for the original system on M. This method has the merit that only one single global Cartesian coordinate system in the ambient space
Rn is used for controller synthesis, and any controller design method in
Rn, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.</abstract><cop>Bognor Regis</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/rnc.4294</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-6496-4189</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1049-8923 |
| ispartof | International journal of robust and nonlinear control, 2018-11, Vol.28 (16), p.4981-4998 |
| issn | 1049-8923 1099-1239 |
| language | eng |
| recordid | cdi_proquest_journals_2119864722 |
| source | Wiley-Blackwell Read & Publish Collection |
| subjects | Cartesian coordinates Control stability Control systems design Controllers Coordinates Design engineering drone Dynamic stability Embedded systems embedding Euclidean geometry Euclidean space manifold Manifolds quadcopter rigid body Rigid structures Synthesis tracking Tracking problem |
| title | On controller design for systems on manifolds in Euclidean space |
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