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Research Papers

A Numerical Method for Solving Fractional Optimal Control Problems Using Ritz Method

[+] Author and Article Information
Ali Nemati

Department of Mathematics,
Payame Noor University,
P.O. Box 19395-3697,
Tehran, Iran
e-mail: ali.nemati83@gmail.com

Sohrab Ali Yousefi

Department of Mathematics,
Shahid Beheshti University, G.C.,
Tehran, Iran
e-mail: s-yousefi@sbu.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 6, 2015; final manuscript received January 25, 2016; published online February 25, 2016. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(5), 051015 (Feb 25, 2016) (7 pages) Paper No: CND-15-1006; doi: 10.1115/1.4032694 History: Received January 06, 2015; Revised January 25, 2016

Our paper presents a new method to solve a class of fractional optimal control problems (FOCPs) based on the numerical polynomial approximation. In the proposed method, the fractional derivative in the dynamical system is considered in the Caputo sense. The approach used here is to approximate the state function by the Legendre orthonormal basis by using the Ritz method. Next, we apply a new constructed operational matrix to approximate fractional derivative of the basis. After transforming the problem into a system of algebraic equations, the problem is solved via the Newton's iterative method. Finally, the convergence of the new method is investigated and some examples are included to illustrate the effectiveness and applicability of the proposed methodology.

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Figures

Grahic Jump Location
Fig. 1

Exact and approximate state and control functions for example 1

Grahic Jump Location
Fig. 2

Exact and approximate state and control functions for example 2

Grahic Jump Location
Fig. 3

Exact and approximate state and control functions for example 3

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