A gradient projection method for solving nonlinear optimal control problems with time-varying delays

Meshkani, Seyed Mojtaba; Effati, Sohrab; Heydari, Aghileh

doi:10.22124/jmm.2025.30121.2691

A gradient projection method for solving nonlinear optimal control problems with time-varying delays

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Payame Noor University, 19395-4697, Tehran, Iran

² Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran

10.22124/jmm.2025.30121.2691

Abstract

An effective numerical method using gradient projection is proposed for solving an optimal control problems that involve time-varying delays in control and state variables. First, a variational inequality is established as necessary conditions. The main idea in variational inequality is to compute the gradient of the objective functional, taking into account time-dependent delays in control and state variables. Then, an iterative scheme utilizing a projection operator is presented, followed by a convergence analysis of the method for a coercive objective functional. At the end, several examples are provided to illustrate that the theoretical finding is efficient.

Keywords