Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems
The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30203/1/30203.pdf |
| _version_ | 1796971693728595968 |
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| author | Tohidi, Emran Soleymani, Fazlollah Kilicman, Adem |
| author_facet | Tohidi, Emran Soleymani, Fazlollah Kilicman, Adem |
| author_sort | Tohidi, Emran |
| collection | UPM |
| description | The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions. |
| first_indexed | 2024-03-06T08:16:48Z |
| format | Article |
| id | upm.eprints-30203 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:16:48Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-302032017-10-20T03:24:08Z http://psasir.upm.edu.my/id/eprint/30203/ Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems Tohidi, Emran Soleymani, Fazlollah Kilicman, Adem The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30203/1/30203.pdf Tohidi, Emran and Soleymani, Fazlollah and Kilicman, Adem (2013) Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems. Abstract and Applied Analysis, 2013. art. no. 535979. pp. 1-9. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/535979/abs/ 10.1155/2013/535979 |
| spellingShingle | Tohidi, Emran Soleymani, Fazlollah Kilicman, Adem Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title | Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title_full | Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title_fullStr | Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title_full_unstemmed | Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title_short | Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems |
| title_sort | robustness of operational matrices of differentiation for solving state space analysis and optimal control problems |
| url | http://psasir.upm.edu.my/id/eprint/30203/1/30203.pdf |
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