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Optimization of Stochastic Jump Diffusion Systems Nonlinear in the Control

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Abstract

We consider the optimal program control problem for a stochastic state- and control-nonlinear jump diffusion system with a given performance functional linear-quadratic in the state. Necessary and sufficient local optimality conditions are obtained, and a numerical procedure for the successive improvement of a given control program is developed. Examples of optimization problems for a switched system with random initial data and terminal invariance are considered as applications.

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Funding

This work was financially supported in part by the Russian Foundation for Basic Research, project no. 20-08-00400.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    M. M. Khrustalev & K. A. Tsarkov

Authors
  1. M. M. Khrustalev
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  2. K. A. Tsarkov
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Correspondence to M. M. Khrustalev or K. A. Tsarkov.

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Translated by V. Potapchouck

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Khrustalev, M.M., Tsarkov, K.A. Optimization of Stochastic Jump Diffusion Systems Nonlinear in the Control. Autom Remote Control 83, 1433–1451 (2022). https://doi.org/10.1134/S0005117922090077

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  • DOI: https://doi.org/10.1134/S0005117922090077

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