A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

Detalhes bibliográficos
Autor(a) principal: Pereira, Fernando Lobo
Data de Publicação: 2010
Outros Autores: Silva, Geraldo Nunes [UNESP]
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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spelling 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

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