A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems. (November 2018)

• Record Type: Journal Article
• Authors: Mohammadi, F; Moradi, L; Baleanu, D; Jajarmi, A
• Is Part Of: Journal of vibration and control. Volume 24:Number 21(2018)
• Page Start: 5030
• Page End: 5043
• Publication Date: 2018-11
• Subjects: Fractional optimal control problems -- hybrid Chelyshkov functions -- fractional calculus -- singular dynamic system -- Gauss–Legendre quadrature; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546317741769
• Languages: English
• ISSNs: 1077-5463

Abstract

In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann–Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs.