On Necessary Optimality Conditions for Singular Controls in Dynamical Systems with a Delay in Control. (18th November 2018)

• Record Type: Journal Article
• Authors: Malik, Samin T.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 15(2018)
• Page Start: 1669
• Page End: 1689
• Publication Date: 2018-11-18
• Subjects: Degenerate singular control -- high-order optimality conditions -- optimal control -- singular control; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1489415
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, an optimal control problem with a delay in control is considered. The second-order necessary condition is obtained for the optimality of singular (in the sense of the maximum principle) control. Also, the notion of degenerate singular control of order k ( k ≥ 1) is introduced and for optimality of this, the high-order necessary condition is obtained. Moreover, while studying the problem, one of the strengthened version of an analog of the maximum principle is shown. Finally, the rich content of the obtained results is illustrated by specific examples.