A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative. (November 2021)

• Record Type: Journal Article
• Authors: Heydari, M.H.; Razzaghi, M.
• Is Part Of: Chaos, solitons and fractals. Volume 152(2021)
• Publication Date: 2021-11
• Subjects: Piecewise fractional derivative -- Piecewise Chebyshev cardinal functions -- Optimal control problems; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111465
• Languages: English
• ISSNs: 0960-0779

Abstract

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.