A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
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Date
2017
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Sage Publications LTD
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Abstract
The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.
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Keywords
Fractional Optimal Control Problem, Legendre Polynomials, Operational Matrix, Lagrange Multiplier Method, Caputo Derivatives
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Citation
Ezz-Eldien, S. S...et al. (2017). "A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems", Journal Of Vibration And Control, Vol. 23, No.1, pp.16-30.
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Source
Journal Of Vibration And Control
Volume
23
Issue
1
Start Page
16
End Page
30