Local Regularity of the Minimum Time Function - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Optimization Theory and Applications Year : 2015

Local Regularity of the Minimum Time Function

Hélène Frankowska
  • Function : Author
  • PersonId : 899311
Luong V. Nguyen
  • Function : Author
  • PersonId : 955523

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.
No file

Dates and versions

hal-00981788 , version 1 (22-04-2014)

Identifiers

Cite

Hélène Frankowska, Luong V. Nguyen. Local Regularity of the Minimum Time Function. Journal of Optimization Theory and Applications, 2015, 164, pp.68-91. ⟨10.1007/s10957-014-0575-x⟩. ⟨hal-00981788⟩
136 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More