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A study on optimal control problem with \(\varepsilon ^{\lambda }-\)error bound for stochastic systems with application to linear quadratic problem

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Abstract

In this paper, we study near-optimal stochastic control problem with \(\varepsilon ^{\lambda }-\)error bound for systems governed by nonlinear controlled Itô stochastic differential equations. The control is allowed to enter into both drift and diffusion coefficients and the control domain need be convex. The proof of our main result is based on Ekeland’s variational principle and some approximation arguments on the state variable and adjoint process with respect to the control variable. Finally, as an example, the linear quadratic control problem is given to illustrate our theoretical results.

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Acknowledgments

The authors would like to thank two anonymous referees for their constructive and insightful comments for improving the quality of this work.

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Authors and Affiliations

  1. Department of Economics, El Oued University, Po Box 145 039000, El Oued, Algeria

    Samira Boukaf

  2. Laboratory of Applied Mathematics, Biskra University, Po Box 145, 07000, Biskra, Algeria

    Mokhtar Hafayed

  3. Department of Mathematics, Bordj Bou Arreridj University, 34000, Bordj-Bou-Arreridj, Algeria

    Messaoud Ghebouli

Authors
  1. Samira Boukaf
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  2. Mokhtar Hafayed
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  3. Messaoud Ghebouli
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Correspondence to Samira Boukaf.

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Boukaf, S., Hafayed, M. & Ghebouli, M. A study on optimal control problem with \(\varepsilon ^{\lambda }-\)error bound for stochastic systems with application to linear quadratic problem. Int. J. Dynam. Control 5, 297–305 (2017). https://doi.org/10.1007/s40435-015-0178-x

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  • DOI: https://doi.org/10.1007/s40435-015-0178-x

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