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

M.H. Heydari and M. Razzaghi

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

Abstract: 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.

Keywords: Piecewise fractional derivative; Piecewise Chebyshev cardinal functions; Optimal control problems (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008195

DOI: 10.1016/j.chaos.2021.111465

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