### Interior sphere property of attainable sets and time optimal control problems

Piermarco Cannarsa, Hélène Frankowska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

This paper studies the attainable set at time for the control system $$\dot{y}\left(t\right)=f(y\left(t\right),u\left(t\right))\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{2.0em}{0ex}}u\left(t\right)\in U$$ showing that, under suitable assumptions on , such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C-regularity for boundaries of attainable sets.