Controllability of control systems on complex simple lie groups and the topology of flag manifolds
Let S be a subsemigroup with nonempty interior of a connected complex simple Lie group G . It is proved that S = G if S contains a subgroup G (α) ≈ Sl (2, ) generated by the exp , where is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of S is co...
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| Veröffentlicht in: | Journal of dynamical and control systems 2013-04, Vol.19 (2), p.157-171 |
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| container_title | Journal of dynamical and control systems |
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| creator | dos Santos, Ariane L. Martin, Luiz A. B. San |
| description | Let
S
be a subsemigroup with nonempty interior of a connected complex simple Lie group
G
. It is proved that
S
=
G
if
S
contains a subgroup
G
(α) ≈ Sl (2,
) generated by the exp
, where
is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of
S
is contractible in some flag manifold if
S
is proper, and exploits the fact that several orbits of
G
(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements. |
| doi_str_mv | 10.1007/s10883-013-9168-5 |
| format | Article |
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S
be a subsemigroup with nonempty interior of a connected complex simple Lie group
G
. It is proved that
S
=
G
if
S
contains a subgroup
G
(α) ≈ Sl (2,
) generated by the exp
, where
is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of
S
is contractible in some flag manifold if
S
is proper, and exploits the fact that several orbits of
G
(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.</description><identifier>ISSN: 1079-2724</identifier><identifier>EISSN: 1573-8698</identifier><identifier>DOI: 10.1007/s10883-013-9168-5</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Calculus of Variations and Optimal Control; Optimization ; Control ; Control systems ; Controllability ; Dynamical Systems ; Dynamical Systems and Ergodic Theory ; Flags ; Invariants ; Lie groups ; Manifolds ; Mathematics ; Mathematics and Statistics ; Orbits ; Roots ; Systems Theory ; Vibration</subject><ispartof>Journal of dynamical and control systems, 2013-04, Vol.19 (2), p.157-171</ispartof><rights>Springer Science+Business Media New York 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-619eb337c0a3dabe128cf7408f2d56125ca50b2c9fc000ca4d1627554f5d60483</citedby><cites>FETCH-LOGICAL-c321t-619eb337c0a3dabe128cf7408f2d56125ca50b2c9fc000ca4d1627554f5d60483</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10883-013-9168-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10883-013-9168-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>dos Santos, Ariane L.</creatorcontrib><creatorcontrib>Martin, Luiz A. B. San</creatorcontrib><title>Controllability of control systems on complex simple lie groups and the topology of flag manifolds</title><title>Journal of dynamical and control systems</title><addtitle>J Dyn Control Syst</addtitle><description>Let
S
be a subsemigroup with nonempty interior of a connected complex simple Lie group
G
. It is proved that
S
=
G
if
S
contains a subgroup
G
(α) ≈ Sl (2,
) generated by the exp
, where
is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of
S
is contractible in some flag manifold if
S
is proper, and exploits the fact that several orbits of
G
(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.</description><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Control systems</subject><subject>Controllability</subject><subject>Dynamical Systems</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Flags</subject><subject>Invariants</subject><subject>Lie groups</subject><subject>Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Orbits</subject><subject>Roots</subject><subject>Systems Theory</subject><subject>Vibration</subject><issn>1079-2724</issn><issn>1573-8698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LxDAUDKKgrv4Abzl6ieajadOjLH7Bghc9hzRNape0qXktuP_erPXsaR7DzPBmELph9I5RWt0Do0oJQpkgNSsVkSfogslKEFXW6jTftKoJr3hxji4B9pTSWgl1gZptHOcUQzBNH_r5gKPHdqUwHGB2A-A4ZmqYgvvG0B8Rh97hLsVlAmzGFs-fDs9xiiF2vwE-mA4PZux9DC1coTNvArjrP9ygj6fH9-0L2b09v24fdsQKzmZSsto1QlSWGtGaxjGurK8KqjxvZcm4tEbShtva2_y9NUXLSl5JWXjZlrRQYoNu19wpxa_FwayHHqzL1UYXF9Cs4LWSkuaNNoitUpsiQHJeT6kfTDpoRvVxT73uqbNWH_fUMnv46oGsHTuX9D4uacyN_jH9AAlteZA</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>dos Santos, Ariane L.</creator><creator>Martin, Luiz A. B. San</creator><general>Springer US</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>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130401</creationdate><title>Controllability of control systems on complex simple lie groups and the topology of flag manifolds</title><author>dos Santos, Ariane L. ; Martin, Luiz A. B. San</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-619eb337c0a3dabe128cf7408f2d56125ca50b2c9fc000ca4d1627554f5d60483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Control systems</topic><topic>Controllability</topic><topic>Dynamical Systems</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Flags</topic><topic>Invariants</topic><topic>Lie groups</topic><topic>Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Orbits</topic><topic>Roots</topic><topic>Systems Theory</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>dos Santos, Ariane L.</creatorcontrib><creatorcontrib>Martin, Luiz A. B. San</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>Civil Engineering Abstracts</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>Journal of dynamical and control systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>dos Santos, Ariane L.</au><au>Martin, Luiz A. B. San</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Controllability of control systems on complex simple lie groups and the topology of flag manifolds</atitle><jtitle>Journal of dynamical and control systems</jtitle><stitle>J Dyn Control Syst</stitle><date>2013-04-01</date><risdate>2013</risdate><volume>19</volume><issue>2</issue><spage>157</spage><epage>171</epage><pages>157-171</pages><issn>1079-2724</issn><eissn>1573-8698</eissn><abstract>Let
S
be a subsemigroup with nonempty interior of a connected complex simple Lie group
G
. It is proved that
S
=
G
if
S
contains a subgroup
G
(α) ≈ Sl (2,
) generated by the exp
, where
is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of
S
is contractible in some flag manifold if
S
is proper, and exploits the fact that several orbits of
G
(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10883-013-9168-5</doi><tpages>15</tpages></addata></record> |
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| ispartof | Journal of dynamical and control systems, 2013-04, Vol.19 (2), p.157-171 |
| issn | 1079-2724 1573-8698 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Calculus of Variations and Optimal Control Optimization Control Control systems Controllability Dynamical Systems Dynamical Systems and Ergodic Theory Flags Invariants Lie groups Manifolds Mathematics Mathematics and Statistics Orbits Roots Systems Theory Vibration |
| title | Controllability of control systems on complex simple lie groups and the topology of flag manifolds |
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