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dc.contributor.authorBarbero Liñán, María
dc.contributor.authorMuñoz Lecanda, Miguel Carlos
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.identifier.citationBarbero Liñán, María; Muñoz Lecanda, Miguel Carlos. “Geometric approach to Pontryagin's Maximum Principle”. Acta Applicandae Mathematicae, 2008, vol. 104, núm. XX, p. XX-XX.
dc.identifier.issn0167-8019 (Print)
dc.identifier.issn1572-9036 (Online)
dc.description.abstractSince the second half of the 20th century, Pontryagin’s Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self–contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.
dc.format.extent56 p.
dc.publisherSpringer Netherlands
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshDifferential equations
dc.subject.lcshMathematical optimization
dc.subject.lcshSystem theory
dc.subject.otherPontryagin's Maximum Principle
dc.subject.otherperturbation vectors
dc.subject.othertangent perturbation cones
dc.subject.otheroptimal control problems
dc.titleGeometric approach to Pontryagin's Maximum Principle
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacOptimització matemàtica
dc.subject.lemacSistemes de control
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34A General theory
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization::49J Existence theories
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization::49K Necessary conditions and sufficient conditions for optimality
dc.subject.amsClassificació AMS::93 Systems Theory; Control::93C Control systems, guided systems
dc.rights.accessOpen Access

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