An Optimal Control for AHomogeneous Linear Dynamical Systems
In this article we introduce an approach to find the optimal control for homogeneous linear dynamical systems. Wei ntroduce the linear quadratic regulator problem for the reduced order model of a dynamical system. We apply the singular perturbation approximations techniques to the original system and...
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An-Najah National University
2018-12-01
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| Series: | مجلة جامعة النجاح للأبحاث العلوم الطبيعية |
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| Online Access: | https://journals.najah.edu/media/journals/full_texts/6_PcGjQVk.pdf |
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| author | Adnan Daraghmeh |
| author_facet | Adnan Daraghmeh |
| author_sort | Adnan Daraghmeh |
| collection | DOAJ |
| description | In this article we introduce an approach to find the optimal control for homogeneous linear dynamical systems. Wei ntroduce the linear quadratic regulator problem for the reduced order model of a dynamical system. We apply the singular perturbation approximations techniques to the original system and obtained our reduced order system. In this paper, our goal is to examine the solution of the problem as the positive parameter ε tends to zero. Our approach that is based on a formal asymptotic expansion of an algebraic Riccati equations associated with the Pontryagin maximum principle. We derive an approximate expressions for the optimal feedback controls. We compute the L2-norm beween the optimal control of the original and reduced system and compare it with the L2-norm of the solution of the Riccati equations of the original and reduced systems. We test the results numerically and obtained a good closed-loop performance for the model reduction. |
| format | Article |
| id | doaj-art-ec6a4e06e7784a9cbc06964121f62df4 |
| institution | DOAJ |
| issn | 1727-2114 2311-8865 |
| language | English |
| publishDate | 2018-12-01 |
| publisher | An-Najah National University |
| record_format | Article |
| series | مجلة جامعة النجاح للأبحاث العلوم الطبيعية |
| spelling | doaj-art-ec6a4e06e7784a9cbc06964121f62df42025-08-20T03:23:35ZengAn-Najah National Universityمجلة جامعة النجاح للأبحاث العلوم الطبيعية1727-21142311-88652018-12-013319311410.35552/anujr.a.33.1.1617An Optimal Control for AHomogeneous Linear Dynamical SystemsAdnan Daraghmeh0Department of Mathematics, Faculty of Sciences, An-Najah National University, Nablus, PalestineIn this article we introduce an approach to find the optimal control for homogeneous linear dynamical systems. Wei ntroduce the linear quadratic regulator problem for the reduced order model of a dynamical system. We apply the singular perturbation approximations techniques to the original system and obtained our reduced order system. In this paper, our goal is to examine the solution of the problem as the positive parameter ε tends to zero. Our approach that is based on a formal asymptotic expansion of an algebraic Riccati equations associated with the Pontryagin maximum principle. We derive an approximate expressions for the optimal feedback controls. We compute the L2-norm beween the optimal control of the original and reduced system and compare it with the L2-norm of the solution of the Riccati equations of the original and reduced systems. We test the results numerically and obtained a good closed-loop performance for the model reduction.https://journals.najah.edu/media/journals/full_texts/6_PcGjQVk.pdfhomogeneoussystemsoptimalcontrolclosed-loop systems.riccatiequation |
| spellingShingle | Adnan Daraghmeh An Optimal Control for AHomogeneous Linear Dynamical Systems مجلة جامعة النجاح للأبحاث العلوم الطبيعية homogeneoussystems optimalcontrol closed-loop systems. riccatiequation |
| title | An Optimal Control for AHomogeneous Linear Dynamical Systems |
| title_full | An Optimal Control for AHomogeneous Linear Dynamical Systems |
| title_fullStr | An Optimal Control for AHomogeneous Linear Dynamical Systems |
| title_full_unstemmed | An Optimal Control for AHomogeneous Linear Dynamical Systems |
| title_short | An Optimal Control for AHomogeneous Linear Dynamical Systems |
| title_sort | optimal control for ahomogeneous linear dynamical systems |
| topic | homogeneoussystems optimalcontrol closed-loop systems. riccatiequation |
| url | https://journals.najah.edu/media/journals/full_texts/6_PcGjQVk.pdf |
| work_keys_str_mv | AT adnandaraghmeh anoptimalcontrolforahomogeneouslineardynamicalsystems AT adnandaraghmeh optimalcontrolforahomogeneouslineardynamicalsystems |