In this paper a semiconcavity result is obtained for the value function of an optimal exit time problem. The related state equation is of general form ẏ(t) = f(y(t), u(t)), y(t) ∈ Rn, u(t) ∈ U ⊂ Rm. However, suitable assumptions are needed relating f with the running and exit costs. The semiconcavity property is then applied to obtain necessary optimality conditions, through the formulation of a suitable version of the Maximum Principle, and to study the singular set of the value function.

Semiconcavity for Optimal Control Problems with Exit Time

PIGNOTTI, CRISTINA;
2000-01-01

Abstract

In this paper a semiconcavity result is obtained for the value function of an optimal exit time problem. The related state equation is of general form ẏ(t) = f(y(t), u(t)), y(t) ∈ Rn, u(t) ∈ U ⊂ Rm. However, suitable assumptions are needed relating f with the running and exit costs. The semiconcavity property is then applied to obtain necessary optimality conditions, through the formulation of a suitable version of the Maximum Principle, and to study the singular set of the value function.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/14627
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