4.6 Article

A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

Journal

JOURNAL OF VIBRATION AND CONTROL
Volume 28, Issue 1-2, Pages 72-82

Publisher

SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546320971156

Keywords

Optimal control problems; fractional Volterra integro-differential equations; discrete Hahn polynomials; operational matrix

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This study develops an efficient numerical method for solving optimal control problems governed by fractional Volterra integro-differential equations, which has advantages in terms of computational cost and complexity.
This study develops an efficient numerical method for optimal control problems governed by fractional Volterra integro-differential equations. A new type of polynomials orthogonal with respect to a discrete norm, namely discrete Hahn polynomials, is introduced and its properties investigated. Fractional operational matrices for the orthogonal polynomials are also derived. A direct numerical algorithm supported by the discrete Hahn polynomials and operational matrices is used to approximate solution of optimal control problems governed by fractional Volterra integro-differential equations. Several examples are analyzed and the results compared with those of other methods. The required CPU time assesses the computational cost and complexity of the proposed method.

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