The focus of this article is the study of discrete optimal control problems (DOCPs) governed by time-varying systems including time-varying delays in control and state variables. Discrete-time optimal control problems 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-delay) 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 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 DOCPs with time-varying multi-delays.

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