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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.