A maximum principle for infinite time asymptotically stable impulsive dynamic control systems
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.3182/20100901-3-IT-2016.00272 http://hdl.handle.net/11449/72096 |
Resumo: | We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC. |
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Repositório Institucional da UNESP |
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A maximum principle for infinite time asymptotically stable impulsive dynamic control systemsControlMaximum principleNecessary conditions of optimalityOptimal stabilityAdjoint variablesAsymptotically stableClosed setControl strategiesConventional systemsDynamic control systemsFinite time intervalsImpulsive controlsInfinite horizonsInfinite timeNon-degeneracyOptimal control problemOptimal impulsive controlTime horizonsControl theoryNonlinear control systemsOptimizationControl system stabilityWe consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.Institute for Systems and Robotics-Porto Faculdade de Engenharia Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 PortoDept. Computer Science and Statistics Universidade Estadual Paulista, 15054-000 - S. J. Rio Preto-SPDept. Computer Science and Statistics Universidade Estadual Paulista, 15054-000 - S. J. Rio Preto-SPUniversidade do PortoUniversidade Estadual Paulista (Unesp)Pereira, Fernando LoboSilva, Geraldo Nunes [UNESP]2014-05-27T11:25:22Z2014-05-27T11:25:22Z2010-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject1326-1331http://dx.doi.org/10.3182/20100901-3-IT-2016.00272IFAC Proceedings Volumes (IFAC-PapersOnline), p. 1326-1331.1474-6670http://hdl.handle.net/11449/7209610.3182/20100901-3-IT-2016.002722-s2.0-800517689753638688119433520Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIFAC Proceedings Volumes (IFAC-PapersOnline)info:eu-repo/semantics/openAccess2021-10-23T21:37:54Zoai:repositorio.unesp.br:11449/72096Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:53:29.898055Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
title |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
spellingShingle |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems Pereira, Fernando Lobo Control Maximum principle Necessary conditions of optimality Optimal stability Adjoint variables Asymptotically stable Closed set Control strategies Conventional systems Dynamic control systems Finite time intervals Impulsive controls Infinite horizons Infinite time Non-degeneracy Optimal control problem Optimal impulsive control Time horizons Control theory Nonlinear control systems Optimization Control system stability |
title_short |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
title_full |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
title_fullStr |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
title_full_unstemmed |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
title_sort |
A maximum principle for infinite time asymptotically stable impulsive dynamic control systems |
author |
Pereira, Fernando Lobo |
author_facet |
Pereira, Fernando Lobo Silva, Geraldo Nunes [UNESP] |
author_role |
author |
author2 |
Silva, Geraldo Nunes [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Porto Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Pereira, Fernando Lobo Silva, Geraldo Nunes [UNESP] |
dc.subject.por.fl_str_mv |
Control Maximum principle Necessary conditions of optimality Optimal stability Adjoint variables Asymptotically stable Closed set Control strategies Conventional systems Dynamic control systems Finite time intervals Impulsive controls Infinite horizons Infinite time Non-degeneracy Optimal control problem Optimal impulsive control Time horizons Control theory Nonlinear control systems Optimization Control system stability |
topic |
Control Maximum principle Necessary conditions of optimality Optimal stability Adjoint variables Asymptotically stable Closed set Control strategies Conventional systems Dynamic control systems Finite time intervals Impulsive controls Infinite horizons Infinite time Non-degeneracy Optimal control problem Optimal impulsive control Time horizons Control theory Nonlinear control systems Optimization Control system stability |
description |
We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-12-01 2014-05-27T11:25:22Z 2014-05-27T11:25:22Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.3182/20100901-3-IT-2016.00272 IFAC Proceedings Volumes (IFAC-PapersOnline), p. 1326-1331. 1474-6670 http://hdl.handle.net/11449/72096 10.3182/20100901-3-IT-2016.00272 2-s2.0-80051768975 3638688119433520 |
url |
http://dx.doi.org/10.3182/20100901-3-IT-2016.00272 http://hdl.handle.net/11449/72096 |
identifier_str_mv |
IFAC Proceedings Volumes (IFAC-PapersOnline), p. 1326-1331. 1474-6670 10.3182/20100901-3-IT-2016.00272 2-s2.0-80051768975 3638688119433520 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
IFAC Proceedings Volumes (IFAC-PapersOnline) |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1326-1331 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128579485040640 |