Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems

Dan Goreac () and Oana-Silvia Serea ()
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Dan Goreac: Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS
Oana-Silvia Serea: Université de Perpignan Via Domitia

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 1, No 2, 22-52

Abstract: Abstract 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 with 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.

Keywords: Optimal stochastic control; Singularly perturbed Brownian diffusions; Occupation measures; Linear programming; 93E20; 49J45; 49L25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-015-0738-4

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