Journal
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF ELECTRICAL ENGINEERING
Volume 44, Issue 4, Pages 1513-1528Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s40998-020-00327-3
Keywords
Fractional optimal control problems; Fractional-order Bernoulli wavelet functions; Operational matrix of fractional integration; Product operational matrix; Lagrange multipliers
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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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