(Almost) Everything you always wanted to know about deterministic control problems in stratified domains

نویسندگان

  • Guy Barles
  • Emmanuel Chasseigne
چکیده

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 . 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. Key-words: Optimal control, discontinuous dynamic, Bellman Equation, viscosity solutions. AMS Class. No: 49L20, 49L25, 35F21.

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عنوان ژورنال:
  • NHM

دوره 10  شماره 

صفحات  -

تاریخ انتشار 2015