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On asymptotic exit-time control problems lacking coercivity∗

Published online by Cambridge University Press:  05 August 2014

M. Motta  and
C. Sartori
M. Motta
Affiliation:
Dipartimento di Matematica, Via Trieste, 63 – 35121 Padova, Italy. motta@math.unipd.it; sartori@math.unipd.it
C. Sartori
Affiliation:
Dipartimento di Matematica, Via Trieste, 63 – 35121 Padova, Italy. motta@math.unipd.it; sartori@math.unipd.it
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Abstract

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.

Keywords

Exit-time problemsimpulsive optimal control problemsviscosity solutionsasymptotic controllability

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 4 , October 2014 , pp. 957 - 982
Copyright
© EDP Sciences, SMAI, 2014

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