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

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

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.

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Main Subjects


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