A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative

In this study, a kind of piecewise fractional derivatives based on the Caputo fractional derivative is used to define a novel category of fractional optimal control problems. The piecewise Chebyshev cardinal functions as an appropriate family of basis functions are considered to construct a numerica...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2021-11, Vol.152, p.111465, Article 111465
Main Authors: Heydari, M.H., Razzaghi, M.
Format: Article
Language:English
Subjects:
Optimal control problems
Piecewise Chebyshev cardinal functions
Piecewise fractional derivative
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Summary:In this study, a kind of piecewise fractional derivatives based on the Caputo fractional derivative is used to define a novel category of fractional optimal control problems. The piecewise Chebyshev cardinal functions as an appropriate family of basis functions are considered to construct a numerical method for solving such problems. The classical and piecewise fractional derivative matrices of these basis functions are derived and used in constructing the proposed technique. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The accuracy of the expressed approach is investigated by solving some examples.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2021.111465