Legendre spectral-collocation method for solving some types of fractional optimal control problems

• Main Authors: Nasser H. Sweilam, Tamer M. Al-Ajami
• Format: Article
• Language: English
• Published: Elsevier 2015-05-01
• Series: Journal of Advanced Research
• Subjects: Legendre spectral-collocation method; Fractional order differential equations; Pontryagin’s maximum principle; Necessary optimality conditions; Rayleigh–Ritz method
• Online Access: http://www.sciencedirect.com/science/article/pii/S2090123214000599

In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques.