Quenching Time Optimal Control for Some Ordinary Differential Equations
This paper concerns time optimal control problems of three different ordinary differential equations in ℝ2. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this s...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/127809 |
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| _version_ | 1832550552680005632 |
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| author | Ping Lin |
| author_facet | Ping Lin |
| author_sort | Ping Lin |
| collection | DOAJ |
| description | This paper concerns time optimal control problems of three different ordinary differential equations in ℝ2. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations. |
| format | Article |
| id | doaj-art-5690c563a0bf430f8c36dd375684a2f1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5690c563a0bf430f8c36dd375684a2f12025-02-03T06:06:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/127809127809Quenching Time Optimal Control for Some Ordinary Differential EquationsPing Lin0School of Mathematics & Statistics, Northeast Normal University, Changchun 130024, ChinaThis paper concerns time optimal control problems of three different ordinary differential equations in ℝ2. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.http://dx.doi.org/10.1155/2014/127809 |
| spellingShingle | Ping Lin Quenching Time Optimal Control for Some Ordinary Differential Equations Journal of Applied Mathematics |
| title | Quenching Time Optimal Control for Some Ordinary Differential Equations |
| title_full | Quenching Time Optimal Control for Some Ordinary Differential Equations |
| title_fullStr | Quenching Time Optimal Control for Some Ordinary Differential Equations |
| title_full_unstemmed | Quenching Time Optimal Control for Some Ordinary Differential Equations |
| title_short | Quenching Time Optimal Control for Some Ordinary Differential Equations |
| title_sort | quenching time optimal control for some ordinary differential equations |
| url | http://dx.doi.org/10.1155/2014/127809 |
| work_keys_str_mv | AT pinglin quenchingtimeoptimalcontrolforsomeordinarydifferentialequations |