Optimal Control of Mechanical Systems
In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the soluti...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Differential Equations and Nonlinear Mechanics |
| Online Access: | http://dx.doi.org/10.1155/2007/18735 |
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| _version_ | 1832552268462817280 |
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| author | Vadim Azhmyakov |
| author_facet | Vadim Azhmyakov |
| author_sort | Vadim Azhmyakov |
| collection | DOAJ |
| description | In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm. |
| format | Article |
| id | doaj-art-00684a043567459990831ee1767bbb18 |
| institution | Kabale University |
| issn | 1687-4099 1687-4102 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Differential Equations and Nonlinear Mechanics |
| spelling | doaj-art-00684a043567459990831ee1767bbb182025-02-03T05:58:58ZengWileyDifferential Equations and Nonlinear Mechanics1687-40991687-41022007-01-01200710.1155/2007/1873518735Optimal Control of Mechanical SystemsVadim Azhmyakov0Departamento de Control Automatico, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico 07360, DF, MexicoIn the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.http://dx.doi.org/10.1155/2007/18735 |
| spellingShingle | Vadim Azhmyakov Optimal Control of Mechanical Systems Differential Equations and Nonlinear Mechanics |
| title | Optimal Control of Mechanical Systems |
| title_full | Optimal Control of Mechanical Systems |
| title_fullStr | Optimal Control of Mechanical Systems |
| title_full_unstemmed | Optimal Control of Mechanical Systems |
| title_short | Optimal Control of Mechanical Systems |
| title_sort | optimal control of mechanical systems |
| url | http://dx.doi.org/10.1155/2007/18735 |
| work_keys_str_mv | AT vadimazhmyakov optimalcontrolofmechanicalsystems |