Discontinuous control problems with state constraints : Linear formulations and dynamic programming principles

Dan Goreac (1) , Carina Ivascu (2)

1 PS
2 Facultatea de Matematica-Informatica

This paper aims at studying a class of discontinuous deterministic control problems under state constraints using a linear programming approach. As for classical control problems (Gaitsgory and Quincampoix (2009), Goreac and Serea (2011)), the primal linear problem is stated on some appropriate space of probability measures. Naturally, the support of these measures is contained in the set of constraints. This linearized value function and its dual can, alternatively, be seen as the limit of standard penalized problems. Second, we provide a semigroup property for this set of probability measures leading to dynamic programming principles for control problems under state constraints. An abstract principle is provided for general bounded costs. Linearized versions are obtained under further (semi)continuity assumptions.

Mots clés: Control under state constraints; Dynamic programming principle; Linear programming; Hamilton-Jacobi equations

Domaines: Optimisation et contrôle [math.OC]

Dan Goreac, Carina Ivascu. Discontinuous control problems with state constraints : Linear formulations and dynamic programming principles. Journal of Mathematical Analysis and Applications, 2013, 402 (2), pp.635--647. ⟨10.1016/j.jmaa.2012.12.043⟩. ⟨hal-00793574⟩