A fractional power series neural network for solving a class of fractional optimal control problems with equality and inequality constraints. (2nd October 2019)

• Record Type: Journal Article
• Authors: Ghasemi, Safiye; Nazemi, Alireza
• Is Part Of: Network. Volume 30:Number 1/4(2019)
• Page Start: 148
• Page End: 175
• Publication Date: 2019-10-02
• Subjects: Fractional optimal control problems -- Pontryagin minimum principle -- Caputo operators -- fractional power series neural network -- unconstrained optimization -- inequality constraints -- stability; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; 006.32
• DOI: 10.1080/0954898X.2019.1693647
• Languages: English
• ISSNs: 0954-898X

Abstract

ABSTRACT: This paper solved fractional order optimal control problems, in which the dynamic control system involves integer and fractional order derivatives with equality and inequality constraints. According to the Pontryagin minimum principle (PMP) for fractional optimal control problem (FOCP) with fractional derivative in the Caputo sense and by constructing a suitable error function, an unconstrained minimization problem is defined. In the optimization problem, trial solutions are used for the states, Lagrange multipliers and control functions where these trial solutions are constructed by fractional power series neural network models. An error function is then minimized using a numerical optimization scheme where weight parameters (or coefficients of the series) and biases associated with all neurons are unknown. Some computational simulations are discussed in details.