We consider both discrete and continuous “uncertain horizon” deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes, explore their connections to infinite-horizon and optimal-stopping problems, and derive sufficient conditions for the applicability of non-iterative (label-setting) methods. In the continuous case, the resulting PDE has a free boundary, on which all characteristic curves originate. The causal properties of “uncertain horizon” problems can be exploited to design efficient numerical algorithms: we derive causal semi-Lagrangian and Eulerian discretizations for the isotropic randomly-terminated problems, and use them to build a modified version of the Fast Marching Method. We illustrate our approach using numerical examples from optimal idle-time processing and expected response-time minimization.
1
Cornell University, Ithaca, USA
2
Cornell University, Ithaca, United States
June Andrews; Alexander Vladimirsky. Deterministic control of randomly-terminated processes. Interfaces and free boundaries, Tome 16 (2014) no. 1, pp. 1-40. doi: 10.4171/ifb/312
@article{10_4171_ifb_312,
author = {June Andrews and Alexander Vladimirsky},
title = {Deterministic control of randomly-terminated processes},
journal = {Interfaces and free boundaries},
pages = {1--40},
year = {2014},
volume = {16},
number = {1},
doi = {10.4171/ifb/312},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/312/}
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