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Interior sphere property of attainable sets and time optimal control problems. (English) Zbl 1105.93007
Summary: This paper studies the attainable set at time \(T>0\) for the control system \[ \dot y(t)=f(y(t),u(t)),\qquad u(t)\in U \] showing that, under suitable assumptions on \(f\), 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 \(C^{1,1}\)-regularity for boundaries of attainable sets.

MSC:
93B03 Attainable sets, reachability
49K15 Optimality conditions for problems involving ordinary differential equations
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