A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems
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- 14 December 2017
- journal article
- research article
- Published by SAGE Publications in Journal of Vibration and Control
- Vol. 24 (21), 5030-5043
- https://doi.org/10.1177/1077546317741769
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.Keywords
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