Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems

Dan Goreac (1) , Oana Silvia Serea (2)

1 PS
2 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

The present paper aims at studying stochastic singularly perturbed control systems. We begin by recalling the linear (primal and dual) formulations for classical control problems. In this framework, we give necessary and sufficient support criteria for optimality of the measures intervening in these formulations. Motivated by these remarks, in a first step, we provide linearized formulations associated to the value function in the averaged dynamics setting. Second, these formulations are used to infer criteria allowing to identify the optimal trajectory of the averaged stochastic system.

Mots clés: Optimal stochastic control; occupation measures; singularly perturbed Brownian diffusions; linear programming

Domaines: Optimisation et contrôle [math.OC]

Dan Goreac, Oana Silvia Serea. Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems. Journal of Optimization Theory and Applications, 2016, 168 (1), pp.22--52. ⟨10.1007/s10957-015-0738-4⟩. ⟨hal-00987521v2⟩