(Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains

G Barles 1, 2 Emmanuel Chasseigne 2, 1
1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 FDP - Fédération de recherche Denis Poisson
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.
Keywords : Key-words: Optimal control Bellman Equation discontinuous dynamic viscosity solutions
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Article dans une revue
Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2015, 10 (4), pp.809-836. 〈http://www.aimsciences.org/journals/〉
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Soumis le : lundi 17 août 2015 - 10:27:23
Dernière modification le : jeudi 7 février 2019 - 17:06:53
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  • ARXIV : 1412.7556

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G Barles, Emmanuel Chasseigne. (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2015, 10 (4), pp.809-836. 〈http://www.aimsciences.org/journals/〉. 〈hal-01097167v3〉

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