Solving infinite-horizon optimalcontrol problems of the time-delayedsystems by a feed forward neural network model. (2nd January 2021)

• Record Type: Journal Article
• Authors: Nazemi, Alireza; Fayyazi, Ensieh
• Is Part Of: Network. Volume 32:Number 1(2021)
• Page Start: 36
• Page End: 63
• Publication Date: 2021-01-02
• Subjects: Infinite-horizon -- time-delayed -- optimal control problems -- approximation -- pontryagin minimum principle -- neural network -- error function -- stability; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; 006.32
• DOI: 10.1080/0954898X.2021.1884762
• Languages: English
• ISSNs: 0954-898X

Abstract

ABSTRACT: A numerical method using neural network for solving infinite-horizon time-delayed optimal control problems is studied. The problem is first transformed, using a Páde approximation, to one without a time-delayed argument. By a suitable change of variable, the obtained non-delay infinite-horizon optimal control problem is converted to a finite-horizon nonlinear optimal control problem. We try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. We then minimize 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.