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arXiv · 1709.07775

Optimality of broken extremals

Andrei A. Agrachev·Carolina Biolo
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Abstract

In this paper we analyse the optimality of broken Pontryagin extremal for an n-dimensional affine control system with a control parameter, taking values in a k- dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the singular locus and the drift does not belong to it. Moreover, if k = 2, we show the optimality of any broken extremal even abnormal when the controllable fields do not form a contact distribution in the point of singularity.

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Andrei A. Agrachev, Carolina Biolo. 2017-09-21. Optimality of broken extremals. https://arxiv.org/abs/1709.07775

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