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Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems

Author

Listed:
  • Dan Goreac

    (Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS)

  • Oana-Silvia Serea

    (Université de Perpignan Via Domitia)

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.

Suggested Citation

  • Dan Goreac & Oana-Silvia Serea, 2016. "Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 22-52, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0738-4
    DOI: 10.1007/s10957-015-0738-4
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    Cited by:

    1. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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