Exit Time Problems in Optimal Control and Vanishing Viscosity Method
Barles, Guy; Perthame, Benoît (1988), Exit Time Problems in Optimal Control and Vanishing Viscosity Method, SIAM Journal on Control and Optimization, 26, 5, p. 1133-1148. http://dx.doi.org/10.1137/0326063
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
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Abstract (EN)The authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first-order Hamilton-Jacobi (HJ) equation up to the boundary. This equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary. When these solutions are equal, they can be obtained through the vanishing viscosity method. Finally, when the HJ equation has a continuous solution, it is proved to be the value function for the first exit time of the domain. It is also the vanishing viscosity limit arising, in particular, in some large deviations problems.
Subjects / Keywordsdeterministic optimal control; exit time; Hamilton-Jacobi equations; viscosity solutions; vanishing viscosity; large deviations
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