(Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains
Analysis of PDEs
2015-08-20 v3 Optimization and Control
Abstract
We revisit the pioneering work of Bressan \& Hong on deterministic control problems in stratified domains, i.e. control problems for which the dynamic and the cost may have discontinuities on submanifolds of R N . By using slightly different methods, involving more partial differential equations arguments, we (i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain a comparison result for general semi-continuous sub and supersolutions (without any continuity assumptions on the value function nor on the sub/supersolutions); (iii) provide a general framework in which a stability result holds.
Cite
@article{arxiv.1412.7556,
title = {(Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains},
author = {G. Barles and Emmanuel Chasseigne},
journal= {arXiv preprint arXiv:1412.7556},
year = {2015}
}