October  2000, 6(4): 975-997. doi: 10.3934/dcds.2000.6.975

Semiconcavity for optimal control problems with exit time

1. 

Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

2. 

Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

3. 

Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica 1, 00133 Roma, Italy

Received  February 2000 Revised  July 2000 Published  August 2000

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

$\dot y(t)=f(y(t),u(t))$,  $y(t)\in\mathbb R^n$, $u(t)\in U\subset \mathbb R^m$.

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.

Citation: Piermarco Cannarsa, Cristina Pignotti, Carlo Sinestrari. Semiconcavity for optimal control problems with exit time. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 975-997. doi: 10.3934/dcds.2000.6.975
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