Pontryagin maximum principle and Stokes theorem

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2019Embargo end date: 01 Dec 2018 Italy English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 142, pages 274-286 (issn: 0393-0440,

Copyright policy )Funded by:MIUR | unidentified

Authors: Cardin F.; Spiro A.;

doi: 10.1016/j.geomphys.2019.04.014 , 10.48550/arxiv.1812.07875

arXiv: 1812.07875

handle: 11581/451406

Pontryagin maximum principle and Stokes theorem

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Abstract

We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived in a new insightful way. It also suggests generalizations in diverse directions of such famous principle.

21 pages, 7 figures; we corrected a few minor misprints, added a couple of references and inserted a new section (Sect. 7); to appear in Journal of Geometry and Physics

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Italy

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Keywords

Mathematics - Differential Geometry, 49J15, 34H05, FOS: Physical sciences, Mathematical Physics (math-ph), Optimality conditions for problems involving ordinary differential equations, principle of minimal labour, Pontryagin maximum principle (PMP), geometric optimal control, Stokes theorem, Differential Geometry (math.DG), Optimization and Control (math.OC), FOS: Mathematics, Mayer problem, Mathematics - Optimization and Control, Mathematical Physics, Control problems involving ordinary differential equations

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