Pontryagin Maximum Principle and Stokes Theorem
Mathematical Physics
2019-06-26 v2 Differential Geometry
math.MP
Optimization and Control
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.
Cite
@article{arxiv.1812.07875,
title = {Pontryagin Maximum Principle and Stokes Theorem},
author = {Franco Cardin and Andrea Spiro},
journal= {arXiv preprint arXiv:1812.07875},
year = {2019}
}
Comments
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