On Necessary Optimality Conditions for Singular Controls in Dynamical Systems with a Delay in Control

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.

KEYWORDS:

• Degenerate singular control
• high-order optimality conditions
• optimal control
• singular control

Additional information

Funding

This research was financially supported by the program “Mathematical modeling of continuous and discrete processes by means of modern computer programs” approved by the resolution no. 7/3 of the Presidium of the Azerbaijan National Academy of Sciences, dated 1 March.