An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems
By Eid H. Doha, Ali H. Bhrawy, Dumitru Băleanu, S. Ezz‐Eldien, Ramy M. Hafez. Advances in Differential Equations, 2015
74 citations recorded by the source corpus.
In this article, we introduce a numerical technique for solving a general form of the fractional optimal control problem. Fractional derivatives are described in the Caputo sense. Using the properties of the shifted Jacobi orthonormal polynomials together with the operational matrix of fractional integrals (described in the Riemann-Liouville sense), we transform the fractional optimal control problem into an equivalent variational problem that can be reduced to a problem consisting of solving a system of algebraic equations by using the Legendre-Gauss quadrature formula with the Rayleigh-Ritz method. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/6bba506163d67a6071381b53c5dec370fc9d965f
How researchers see this paper
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In Applied Mathematics
- Amin Jajarmi
- Dumitru Băleanu
- Thabet Abdeljawad
- Arran Fernandez
- Fahd Jarad
- Behzad Ghanbari
- Xiao-jun Yang
- Pshtiwan Othman Mohammed
In Modeling and Simulation
- Amin Jajarmi
- Dumitru Băleanu
- Fakhrodin Mohammadi
- Leila Moradi
- Thabet Abdeljawad
- Arran Fernandez
- Behzad Ghanbari
- Mehmet Yavuz
In Numerical Analysis
- Amin Jajarmi
- Dumitru Băleanu
- Fakhrodin Mohammadi
- Leila Moradi
- Arran Fernandez
- Thabet Abdeljawad
- Behzad Ghanbari
- Pshtiwan Othman Mohammed
Citations in the corpus
- An iterative approach for solving fractional optimal control problems (2018, unknown): “…2012), Tricaud and Chen (2010), Lotfi et al. (2011), Yousefi et al. (2011), Jarad et al. (2012), Akbarian and Keyanpour (2013), Alipour et al. (2013), Lotfi and Yousefi (2013), Pooseh et al. (2013), Bhrawy et al. (2015a); Bhrawy et al. (2015b), Doha et al. (2015), and the references cited therein.”
- A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems (2017, methodology): “Doha et al. (2015) presented a numerical technique based on shifted orthonormal Jacobi polynomials for solving a general form of FOCPs.”