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 problems, impulsive optimal control problems, viscosity solutions, asymptotic controllability

@article{COCV_2014__20_4_957_0, author = {Motta, M. and Sartori, C.}, title = {On asymptotic exit-time control problems lacking coercivity}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {957--982}, publisher = {EDP-Sciences}, volume = {20}, number = {4}, year = {2014}, doi = {10.1051/cocv/2014003}, mrnumber = {3264230}, zbl = {1301.49006}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014003/} }

TY - JOUR AU - Motta, M. AU - Sartori, C. TI - On asymptotic exit-time control problems lacking coercivity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 957 EP - 982 VL - 20 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014003/ DO - 10.1051/cocv/2014003 LA - en ID - COCV_2014__20_4_957_0 ER -

%0 Journal Article %A Motta, M. %A Sartori, C. %T On asymptotic exit-time control problems lacking coercivity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 957-982 %V 20 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014003/ %R 10.1051/cocv/2014003 %G en %F COCV_2014__20_4_957_0

Motta, M.; Sartori, C. On asymptotic exit-time control problems lacking coercivity. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 4, pp. 957-982. doi : 10.1051/cocv/2014003. http://archive.numdam.org/articles/10.1051/cocv/2014003/

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