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dc.contributor.authorTrélat, E.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-06-13T13:33:49Z
dc.date.available2016-06-13T13:33:49Z
dc.date.issued2014-12-31
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/20.500.11824/234
dc.description.abstractTurnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleThe turnpike property infinite-dimensional nonlinear optimal control
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.jde.2014.09.005
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0022039614003568
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/246775en_US
dc.relation.projectIDES/6PN/MTM2011-29306-C02-01en_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleJournal of Differential Equationsen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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