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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 9
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Articles

Differential inclusions with mean derivatives having extreme right-hand sides and optimal control

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Pages 2020-2028 | Received 21 Aug 2019, Accepted 16 Sep 2019, Published online: 07 Oct 2019
 

Abstract

First we prove the existence of solutions of some special stochastic differential inclusion with mean derivatives having lower semi-continuous right-hand sides that may not be convex. Then we show that among those solutions there is a solution that minimizes a certain cost criterion. After that this result is applied to investigation of controlled stochastic differential equations with feed back, whose right-hand sides take values in extreme sets of Hausdorff continuous set-valued vector field with bounded convex images. By reducing the equation to the inclusion of above-mentioned sort we prove that there exists a control that realizes the optimal solution of the inclusion as an optimal solution of the equation (an analogue of Filippov's theorem).

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is supported in part by RFBR Grant 18–01–00048.

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