Geometric approach to Pontryagin's Maximum Principle
Cita com:
hdl:2117/1987
Tipus de documentArticle
Data publicació2008-10
EditorSpringer Netherlands
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
Since 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.
CitacióBarbero Liñán, María; Muñoz Lecanda, Miguel Carlos. “Geometric approach to Pontryagin's Maximum Principle”. Acta Applicandae Mathematicae, 2008, vol. 104, núm. XX, p. XX-XX.
ISSN0167-8019 (Print)
1572-9036 (Online)
1572-9036 (Online)
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