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## 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 | ||

مقاله 40، دوره 3، شماره 3، مهر 2020، صفحه 337-351
اصل مقاله (1.61 MB)
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نوع مقاله: Research Articles | ||

شناسه دیجیتال (DOI): 10.22111/ieco.2020.31807.1215 | ||

نویسندگان | ||

Azar Shabani^{1}؛ Alireza Fatehi ^{} ^{} ^{2}؛ Fahimeh Soltanian ^{} ^{} ^{3}؛ Reza Jamilnia^{4}
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^{1}Department of Mathematics, Payame Noor University, Tehren, Iran | ||

^{2}APAC Research Group, Faculty of Electrical Eng., K.N. Toosi University of Technology, Tehran, Iran | ||

^{3}Department of Mathematics, Payame Noor University, Tehran, Iran | ||

^{4}Department of Mechanical Engineering, University of Guilan, Rasht, Iran. | ||

چکیده | ||

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 | ||

کلیدواژهها | ||

differential-algebraic equations؛ semi-analytical homotopy perturbation method؛ least squares method؛ span set؛ optimal control | ||

مراجع | ||

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