Geometric Approach to Pontryagin’s Maximum Principle

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 geo...

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Podrobná bibliografie
Vydáno v:	Acta applicandae mathematicae Ročník 108; číslo 2; s. 429 - 485
Hlavní autoři:	Barbero-Liñán, M., Muñoz-Lecanda, M. C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Dordrecht Springer Netherlands 01.11.2009 Springer Nature B.V
Témata:	34 Ordinary differential equations 34A General theory 49 Calculus of variations and optimal control; optimization 49J Existence theories 49K Necessary conditions and sufficient conditions for optimality 93 Systems Theory; Control 93C Control systems, guided systems Aircraft Applications of Mathematics Applied mathematics Calculus of Variations and Optimal Control; Optimization Classificació AMS Computational Mathematics and Numerical Analysis Control Control theory Differential equations Equacions diferencials ordinàries Flow control Geometry Mathematical analysis Mathematical optimization Mathematics Mathematics and Statistics optimal control problems Optimització matemàtica Optimization Partial Differential Equations perturbation vectors Pontryagin's Maximum Principle Probability Theory and Stochastic Processes Robotics Sistemes de control Studies System theory tangent perturbation cones 49J30 Optimal control problems 34A12 93C15 Pontryagin’s maximum principle Perturbation vectors 49K05 49K15 Tangent perturbation cones 49J15
ISSN:	0167-8019, 1572-9036, 1572-9036
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Popis
Shrnutí:	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.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0167-8019 1572-9036 1572-9036
DOI:	10.1007/s10440-008-9320-5