An efficient design for solving discrete optimal control problem with time-varying multi-delays

Iranian Journal of Numerical Analysis and Optimization

مقاله 12، دوره 12، Issue 3 (Special Issue) - شماره پیاپی 23، بهمن 2022، صفحه 719-738   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.78220.1168

نویسندگان

S.M. Abdolkhaleghzade؛ S. Effati^* ؛ S.A. Rakhshan

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

The focus of this article is on the study of discrete optimal control problems (DOCPs) governed by time-varying systems, including time-varying delays in control and state variables. DOCPs arise naturally in many multi-stage control and inventory problems where time enters discretely in a natural fashion. Here, the Euler--Lagrange formulation (which are two-point boundary values with time-varying multi-delays) is employed as an efficient technique to solve DOCPs with time-varying multi-delays. The main feature of the procedure is converting the complex version of the discrete-time optimal control problem into a simple form of differential equations. Since the main problem is in discrete form, then the Euler--Lagrange equation changes to an algebraic system with initial and final conditions. The graphic representation of numerical simulation results shows that the proposed method can effectively and reliably solve DOCPs with time-varying multi-delays.

کلیدواژه‌ها

Discrete-time optimal control problem with time-varying delay؛ Euler–Lagrange equations؛ Pontryagin maximum principle

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