Local Regularity of the Minimum Time Function

Hélène Frankowska () and Luong V. Nguyen ()
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Hélène Frankowska: CNRS, IMJ-PRG, UMR 7586, Sorbonne Universités, UPMC Univ Paris 06, Univ Paris Diderot Sorbonne Paris Cité
Luong V. Nguyen: Università di Padova

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 1, No 3, 68-91

Abstract: Abstract We consider the minimum time problem of optimal control theory. It is well known that under appropriate controllability type conditions the minimum time function has an open domain of definition and is locally Lipschitz on it. Thus, it is differentiable almost everywhere on its domain. Furthermore, in general, it fails to be differentiable at points where there are multiple time optimal trajectories and its differentiability at a point does not guarantee continuous differentiability around this point. In this paper, however, we show that, under some regularity assumptions, the nonemptiness of proximal subdifferential of the minimum time function at a point implies its continuous differentiability on a neighborhood of this point.

Keywords: Hamiltonian systems; Conjugate times; Maximum principle; Minimum time function; 49N60; 49J15; 49K15 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0575-x

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