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Optimization of Nonlinear Systems of Stochastic Difference Equations

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Ukrainian Mathematical Journal Aims and scope

Abstract

We present new results concerning the synthesis of optimal control for systems of difference equations that depend on a semi-Markov or Markov stochastic process. We obtain necessary conditions for the optimality of solutions that generalize known conditions for the optimality of deterministic systems of control. These necessary optimality conditions are obtained in the form convenient for the synthesis of optimal control. On the basis of Lyapunov stochastic functions, we obtain matrix difference equations of the Riccati type, the integration of which enables one to synthesize an optimal control. The results obtained generalize results obtained earlier for deterministic systems of difference equations.

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Authors and Affiliations

  1. Kiev National Economic University, Kiev

    K. G. Valeev & I. A. Dzhalladova

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  1. K. G. Valeev
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  2. I. A. Dzhalladova
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Valeev, K.G., Dzhalladova, I.A. Optimization of Nonlinear Systems of Stochastic Difference Equations. Ukrainian Mathematical Journal 54, 1–16 (2002). https://doi.org/10.1023/A:1019788317523

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  • DOI: https://doi.org/10.1023/A:1019788317523

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