Differential inclusions with mean derivatives having extreme right-hand sides and optimal control. Issue 9 (4th July 2021)

• Record Type: Journal Article
• Authors: Gliklikh, Yuri E.; Zheltikova, Olga O.
• Is Part Of: Applicable analysis. Volume 100:Issue 9(2021)
• Page Start: 2020
• Page End: 2028
• Publication Date: 2021-07-04
• Subjects: Mean derivatives -- stochastic differential inclusions -- decomposable set-valued mappings -- extreme points -- controlled stochastic differential equations -- optimal solutions; 60H10 -- 47H04 -- 34A60 -- 60H30 -- 60K30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1672870
• Languages: English
• ISSNs: 0003-6811

Abstract

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).