An efficient pseudospectral method for solving a class of nonlinear optimal control problems
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called...
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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/30214/ http://psasir.upm.edu.my/id/eprint/30214/1/30214.pdf |
| _version_ | 1848846613900951552 |
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| author | Tohidi, Emran Pasban, Atena Kilicman, Adem Noghabi, S. Lotfi |
| author_facet | Tohidi, Emran Pasban, Atena Kilicman, Adem Noghabi, S. Lotfi |
| author_sort | Tohidi, Emran |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea. |
| first_indexed | 2025-11-15T09:05:30Z |
| format | Article |
| id | upm-30214 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:30Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-302142017-10-20T03:20:48Z http://psasir.upm.edu.my/id/eprint/30214/ An efficient pseudospectral method for solving a class of nonlinear optimal control problems Tohidi, Emran Pasban, Atena Kilicman, Adem Noghabi, S. Lotfi This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30214/1/30214.pdf Tohidi, Emran and Pasban, Atena and Kilicman, Adem and Noghabi, S. Lotfi (2013) An efficient pseudospectral method for solving a class of nonlinear optimal control problems. Abstract and Applied Analysis, 2013. art. no. 357931. pp. 1-7. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/357931/ 10.1155/2013/357931 |
| spellingShingle | Tohidi, Emran Pasban, Atena Kilicman, Adem Noghabi, S. Lotfi An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title | An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title_full | An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title_fullStr | An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title_full_unstemmed | An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title_short | An efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| title_sort | efficient pseudospectral method for solving a class of nonlinear optimal control problems |
| url | http://psasir.upm.edu.my/id/eprint/30214/ http://psasir.upm.edu.my/id/eprint/30214/ http://psasir.upm.edu.my/id/eprint/30214/ http://psasir.upm.edu.my/id/eprint/30214/1/30214.pdf |