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On control of two-scale stochastic systems with linear dynamics in the fast variables

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Abstract

We consider a problem of optimal control for a stochastic two-scale system that depends on a small positive parameterɛ and where the stochastic differential equations, describing the evolution of the fast variables, degenerate to algebraic equations in the limit whenɛ=0. The model is nonlinear, but with the fast components entering linearly. Our main result is to show that, whenɛ tends to zero, the optimal value of the cost functional, that also includes the fast variables in the terminal pay-off, converges to the optimal value of a suitable reduced stochastic control problem. As a consequence we also have that a nearly optimal control for the limit problem can be modified to become nearly optimal also for the prelimit problems whenɛ. is sufficiently small.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, 32 Krasikova Street, 117418, Moscow, Russia

    Yuri M Kabanov

  2. Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, F-25030, Besançon Cedex, France

    Yuri M Kabanov

  3. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, Padova, Italy

    Wolfgang J. Runggaldier

Authors
  1. Yuri M Kabanov
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  2. Wolfgang J. Runggaldier
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Additional information

The work by Yuri M. Kabanov was performed during a stay in Padova supported by GNAFA/CNR.

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Kabanov, Y.M., Runggaldier, W.J. On control of two-scale stochastic systems with linear dynamics in the fast variables. Math. Control Signal Systems 9, 107–122 (1996). https://doi.org/10.1007/BF01211749

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  • DOI: https://doi.org/10.1007/BF01211749

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