On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems
In this paper, two semi-analytical techniques are introduced to compute the solutions of differential-algebraic equations (DAEs), called the Least Squares Repetitive Homotopy Perturbation Method (LSRHPM) and the Least Squares Span Repetitive Homotopy Perturbation Method (LSSRHPM). The truncated seri...
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| Format: | Article |
| Language: | English |
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University of Sistan and Baluchestan
2020-07-01
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| Series: | International Journal of Industrial Electronics, Control and Optimization |
| Subjects: | |
| Online Access: | https://ieco.usb.ac.ir/article_5276_1e95029fe1cf4cfceaffe724769b8dd8.pdf |
| _version_ | 1811306276615880704 |
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| author | Azar Shabani Alireza Fatehi Fahimeh Soltanian Reza Jamilnia |
| author_facet | Azar Shabani Alireza Fatehi Fahimeh Soltanian Reza Jamilnia |
| author_sort | Azar Shabani |
| collection | DOAJ |
| description | In this paper, two semi-analytical techniques are introduced to compute the solutions of differential-algebraic equations (DAEs), called the Least Squares Repetitive Homotopy Perturbation Method (LSRHPM) and the Least Squares Span Repetitive Homotopy Perturbation Method (LSSRHPM). The truncated series solution by the homotopy perturbation method only is suitable for small-time intervals. Therefore, to extend it for long time intervals, we consider the Repetitive Homotopy Perturbation Method (RHPM). To improve the accuracy of the solutions obtained by RHPM and to reduce the residual errors, least squares methods and span set are combined with RHPM. The proposed methods are applied to solve nonlinear differential-algebraic equations and optimal control problems. The results of the proposed methods are compared using some illustrative examples. The obtained results demonstrate the effectiveness and high accuracy of the new modifications. The effect of the parameters on the accuracy and performance of the methods are studied through some illustrative examples |
| first_indexed | 2024-04-13T08:42:36Z |
| format | Article |
| id | doaj.art-c2b2890e20c8452b94fd7aa6863c9fad |
| institution | Directory Open Access Journal |
| issn | 2645-3517 2645-3568 |
| language | English |
| last_indexed | 2024-04-13T08:42:36Z |
| publishDate | 2020-07-01 |
| publisher | University of Sistan and Baluchestan |
| record_format | Article |
| series | International Journal of Industrial Electronics, Control and Optimization |
| spelling | doaj.art-c2b2890e20c8452b94fd7aa6863c9fad2022-12-22T02:53:51ZengUniversity of Sistan and BaluchestanInternational Journal of Industrial Electronics, Control and Optimization2645-35172645-35682020-07-013333735110.22111/ieco.2020.31807.12155276On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problemsAzar Shabani0Alireza Fatehi1Fahimeh Soltanian2Reza Jamilnia3Department of Mathematics, Payame Noor University, Tehren, IranAPAC Research Group, Faculty of Electrical Eng., K.N. Toosi University of Technology, Tehran, IranDepartment of Mathematics, Payame Noor University, Tehran, IranDepartment of Mechanical Engineering, University of Guilan, Rasht, Iran.In this paper, two semi-analytical techniques are introduced to compute the solutions of differential-algebraic equations (DAEs), called the Least Squares Repetitive Homotopy Perturbation Method (LSRHPM) and the Least Squares Span Repetitive Homotopy Perturbation Method (LSSRHPM). The truncated series solution by the homotopy perturbation method only is suitable for small-time intervals. Therefore, to extend it for long time intervals, we consider the Repetitive Homotopy Perturbation Method (RHPM). To improve the accuracy of the solutions obtained by RHPM and to reduce the residual errors, least squares methods and span set are combined with RHPM. The proposed methods are applied to solve nonlinear differential-algebraic equations and optimal control problems. The results of the proposed methods are compared using some illustrative examples. The obtained results demonstrate the effectiveness and high accuracy of the new modifications. The effect of the parameters on the accuracy and performance of the methods are studied through some illustrative exampleshttps://ieco.usb.ac.ir/article_5276_1e95029fe1cf4cfceaffe724769b8dd8.pdfdifferential-algebraic equationssemi-analytical homotopy perturbation methodleast squares methodspan setoptimal control |
| spellingShingle | Azar Shabani Alireza Fatehi Fahimeh Soltanian Reza Jamilnia On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems International Journal of Industrial Electronics, Control and Optimization differential-algebraic equations semi-analytical homotopy perturbation method least squares method span set optimal control |
| title | On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems |
| title_full | On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems |
| title_fullStr | On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems |
| title_full_unstemmed | On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems |
| title_short | On the coupling of least squares method and homotopy perturbation method for the solution of differential-algebraic equations and its applications in optimal control problems |
| title_sort | on the coupling of least squares method and homotopy perturbation method for the solution of differential algebraic equations and its applications in optimal control problems |
| topic | differential-algebraic equations semi-analytical homotopy perturbation method least squares method span set optimal control |
| url | https://ieco.usb.ac.ir/article_5276_1e95029fe1cf4cfceaffe724769b8dd8.pdf |
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