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An efficient approximate method for solving delay fractional optimal control problems

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Abstract

In this paper, a new numerical method for solving the delay fractional optimal control problems (DFOCPs) with quadratic performance index is presented. In the discussed DFOCP, the fractional derivative is considered in the Caputo sense. The method is based upon the Bernoulli wavelets basis. To solve the problem, first the DFOCP is transformed into an equivalent problem with dynamical system without delay. Then, an operational matrix of Riemann–Liouville fractional integration based on Bernoulli wavelets is introduced and is utilized to reduce the problem to the solution of a system of algebraic equations. With the aid of Gauss–Legendre integration formula and Newton’s iterative method for solving a system of algebraic equations, the problem is solved approximately. Also, the convergence of the Bernoulli wavelet basis is obtained. Finally, some examples are given to demonstrate the validity and applicability of the new technique and a comparison is made with the existing results.

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Acknowledgments

Authors are very grateful to one of the reviewers for carefully reading the paper and for his(her) comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    P. Rahimkhani & Y. Ordokhani

  2. Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

    E. Babolian

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  1. P. Rahimkhani
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  2. Y. Ordokhani
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  3. E. Babolian
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Correspondence to Y. Ordokhani.

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Rahimkhani, P., Ordokhani, Y. & Babolian, E. An efficient approximate method for solving delay fractional optimal control problems. Nonlinear Dyn 86, 1649–1661 (2016). https://doi.org/10.1007/s11071-016-2983-y

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