Reflected dynamics: Viscosity analysis for L ∞ cost, relaxation and abstract dynamic programming

Dan Goreac (1, 2) , Hadjer Hechaichi (3) , Oana-Silvia Serea (4, 3)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
2 Shandong University
3 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
4 Western Norway University of Applied Sciences

We study an optimal control problem consisting in minimizing the L ∞ norm of a Borel measurable cost function, in finite time, and over all trajectories associated with a controlled dynamics which is reflected in a compact prox-regular set. The first part of the paper provides the viscosity characterization of the value function for uniformly continuous costs. The second part is concerned with linear programming formulations of the problem and the ensued byproducts as e.g. dynamic programming principle for merely measurable costs.

Domaines: Optimisation et contrôle [math.OC]

Dan Goreac, Hadjer Hechaichi, Oana-Silvia Serea. Reflected dynamics: Viscosity analysis for L ∞ cost, relaxation and abstract dynamic programming. Journal of Differential Equations, 2021, 290, pp.78-115. ⟨10.1016/j.jde.2021.04.024⟩. ⟨hal-03214190⟩