Solving optimal control problems of the time-delayed systems by a neural network framework. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Nazemi, Alireza; Fayyazi, Ensieh; Mortezaee, Marzieh
• Is Part Of: Connection science. Volume 31:Issue 4(2019)
• Page Start: 342
• Page End: 372
• Publication Date: 2019-10-02
• Subjects: Time-delayed -- optimal control problems -- approximation -- Pontryagin minimum principle -- neural network -- error function -- stability -- convergent; Neural computers -- Periodicals; Artificial intelligence -- Periodicals; Cognitive science -- Periodicals; Connectionism -- Periodicals; 006.3
• DOI: 10.1080/09540091.2019.1604627
• Languages: English
• ISSNs: 0954-0091

Abstract

ABSTRACT: A numerical method using neural networks for solving time-delayed optimal control problems is studied. The problem is first transformed into one without a time-delayed argument, using a Páde approximation. We try to approximate the solution of the Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. We then minimise the error function where weights and biases associated with all neurons are unknown. Substituting the optimal values of the weights and biases in the trial solutions, we obtain the optimal solution of the original problem. Several examples are given to show the efficiency of the method.