Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 9
47
Views
1
CrossRef citations to date
0
Altmetric
Articles

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

&
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).

AMS Subject Classifications:

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.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.