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Numerical Solution of Fractional Optimal Control Problems with Inequality Constraint Using the Fractional-Order Bernoulli Wavelet Functions

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Abstract

This paper studies the fractional optimal control problems (FOCPs) with inequality constraints. Using the Caputo definition, an optimization method based on a set of basis functions, namely the fractional-order Bernoulli wavelet functions (F-BWFs), is proposed. The solution is expanded in terms of the F-BWFs with unknown coefficients. In the first step, we convert the inequality conditions to equality conditions. In the second step, we use the operational matrix (OM) of fractional integration and the product OM of F-BWFs, with the help of the Lagrange multipliers technique for converting the FOCPs into an easier one, described by a system of nonlinear algebraic equations. Finally, for illustrating the efficiency and accuracy of the proposed technique, several numerical examples are analysed and the results compared with the analytical or the approximate solutions obtained by other techniques.

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Acknowledgements

The authors are very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Forugh Valian & Mohammad Ali Vali

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

    Yadollah Ordokhani

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  1. Forugh Valian
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Valian, F., Ordokhani, Y. & Vali, M.A. Numerical Solution of Fractional Optimal Control Problems with Inequality Constraint Using the Fractional-Order Bernoulli Wavelet Functions. Iran J Sci Technol Trans Electr Eng 44, 1513–1528 (2020). https://doi.org/10.1007/s40998-020-00327-3

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