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Approximation methods for solving fractional optimal control problems

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Abstract

In this review paper, approximation methods for the free final time of fractional optimal control problems (FOCPs) are displayed. The considered problems mainly include the fractional differential equations (FDEs) with fractional derivatives (FDs). In this way, the considered tools and techniques mainly include the necessary optimal conditions in the form of two-point boundary value (TPBV) problem of fractional order. The Legendre operational, Ritz method and the Jacobi, Bernoulli and Legendre polynomials are extended as numerical methods for FOCPs accordingly. At the same time, the techniques for improving the accuracy and computation and storage are also introduced.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Samaneh Soradi Zeid, Sohrab Effati & Ali Vahidian Kamyad

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  1. Samaneh Soradi Zeid
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  2. Sohrab Effati
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  3. Ali Vahidian Kamyad
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Correspondence to Sohrab Effati.

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Communicated by Jose Roberto Castilho Piqueira, Elbert E N Macau, Luiz de Siqueira Martins Filho.

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Zeid, S.S., Effati, S. & Kamyad, A.V. Approximation methods for solving fractional optimal control problems. Comp. Appl. Math. 37 (Suppl 1), 158–182 (2018). https://doi.org/10.1007/s40314-017-0424-2

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  • DOI: https://doi.org/10.1007/s40314-017-0424-2

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