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Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation

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Abstract

We present an exactly soluble optimal stochastic control problem involving a diffusive two-states random evolution process and connect it to a nonlinear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between the non-linear Boltzmann-like equations introduced by Ruijgrok and Wu and the optimal control of a two-states random evolution process. In the sense of this generalization, the nonlinear reaction-diffusion equation is identified as the natural diffusive generalization of the Ruijgrok–Wu and Boltzmann model.

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Authors and Affiliations

  1. CCM, Universidade da Madeira, Funchal, Portugal

    R. Filliger & L. Streit

  2. Institut de Production et Robotique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    M.-O. Hongler

Authors
  1. R. Filliger
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  2. M.-O. Hongler
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  3. L. Streit
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Corresponding author

Correspondence to R. Filliger.

Additional information

Communicated by R. Glowinski.

This work was partially supported by Fonds National pour la Recherche Suisse and Fundaçao para a Ciência e a Tecnologica FCT, FEDER/POCTI-SFA-1-219, Portugal.

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Filliger, R., Hongler, MO. & Streit, L. Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation. J Optim Theory Appl 137, 497–505 (2008). https://doi.org/10.1007/s10957-007-9346-2

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  • DOI: https://doi.org/10.1007/s10957-007-9346-2

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