﻿ A Neural Network Method Based on Mittag-Leffler Function for Solving a Class of Fractional Optimal Control Problems

# A Neural Network Method Based on Mittag-Leffler Function for Solving a Class of Fractional Optimal Control Problems

##### نویسندگان
• Alireza Nazemi Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
• safiye Ghasemi Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Tel-Fax No:+9823-32300235, Shahrood, Iran,
##### چکیده

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for the states, Lagrange multipliers and control functions where these trial solutions are constructed by a feed forward neural network model. We then minimize the error function using a numerical optimization scheme where weight parameters and biases associated with all neurons are unknown. Some examples are included to demonstrate the validity and capability of the proposed method. The strength of the proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Another advantage of the presented approach is to provide results on entire finite continuous domain unlike some other numerical methods which provides solutions only on discrete grid of point. In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for the states, Lagrange multipliers and control functions where these trial solutions are constructed by a neural network model.

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عنوان ژورنال:

دوره 50  شماره 2

صفحات  131- 140

تاریخ انتشار 2018-12-01

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