Designing the sinc neural networks to solve the fractional optimal control problem
Sinc numerical methods are essential approaches for solving nonlinear problems. In this work, based on this method, the sinc neural networks (SNNs) are designed and applied to solve the fractional optimal control problem (FOCP) in the sense of the Riemann–Liouville (RL) derivative. To solve the FOCP...
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| Format: | Article |
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Ferdowsi University of Mashhad
2024-12-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
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| Online Access: | https://ijnao.um.ac.ir/article_45196_621d8d6516c4ea0aff9c8a92689768ed.pdf |
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| author | R. Heydari Dastjerdi G. Ahmadi |
| author_facet | R. Heydari Dastjerdi G. Ahmadi |
| author_sort | R. Heydari Dastjerdi |
| collection | DOAJ |
| description | Sinc numerical methods are essential approaches for solving nonlinear problems. In this work, based on this method, the sinc neural networks (SNNs) are designed and applied to solve the fractional optimal control problem (FOCP) in the sense of the Riemann–Liouville (RL) derivative. To solve the FOCP, we first approximate the RL derivative using Grunwald–Letnikov operators. Then, according to Pontryagin’s minimum principle for FOCP and using an error function, we construct an unconstrained minimization problem. We approximate the solution of the ordinary differential equation obtained from the Hamiltonian condition using the SNN. Simulation results show the efficiencies of the proposed approach. |
| format | Article |
| id | doaj-art-5f8d8ee3854540f2b93ce47bfcd25ffb |
| institution | OA Journals |
| issn | 2423-6977 2423-6969 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj-art-5f8d8ee3854540f2b93ce47bfcd25ffb2025-08-20T02:21:02ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692024-12-0114Issue 41016103610.22067/ijnao.2024.86494.138045196Designing the sinc neural networks to solve the fractional optimal control problemR. Heydari Dastjerdi0G. Ahmadi1Department of Mathematics, Payame Noor University, Tehran, Iran.Department of Mathematics, Payame Noor University, Tehran, Iran.Sinc numerical methods are essential approaches for solving nonlinear problems. In this work, based on this method, the sinc neural networks (SNNs) are designed and applied to solve the fractional optimal control problem (FOCP) in the sense of the Riemann–Liouville (RL) derivative. To solve the FOCP, we first approximate the RL derivative using Grunwald–Letnikov operators. Then, according to Pontryagin’s minimum principle for FOCP and using an error function, we construct an unconstrained minimization problem. We approximate the solution of the ordinary differential equation obtained from the Hamiltonian condition using the SNN. Simulation results show the efficiencies of the proposed approach.https://ijnao.um.ac.ir/article_45196_621d8d6516c4ea0aff9c8a92689768ed.pdfsinc numerical methodneural networksinc neural networkpontryagin’s minimum principlefractional optimal control problem |
| spellingShingle | R. Heydari Dastjerdi G. Ahmadi Designing the sinc neural networks to solve the fractional optimal control problem Iranian Journal of Numerical Analysis and Optimization sinc numerical method neural network sinc neural network pontryagin’s minimum principle fractional optimal control problem |
| title | Designing the sinc neural networks to solve the fractional optimal control problem |
| title_full | Designing the sinc neural networks to solve the fractional optimal control problem |
| title_fullStr | Designing the sinc neural networks to solve the fractional optimal control problem |
| title_full_unstemmed | Designing the sinc neural networks to solve the fractional optimal control problem |
| title_short | Designing the sinc neural networks to solve the fractional optimal control problem |
| title_sort | designing the sinc neural networks to solve the fractional optimal control problem |
| topic | sinc numerical method neural network sinc neural network pontryagin’s minimum principle fractional optimal control problem |
| url | https://ijnao.um.ac.ir/article_45196_621d8d6516c4ea0aff9c8a92689768ed.pdf |
| work_keys_str_mv | AT rheydaridastjerdi designingthesincneuralnetworkstosolvethefractionaloptimalcontrolproblem AT gahmadi designingthesincneuralnetworkstosolvethefractionaloptimalcontrolproblem |