| 一类二阶常微分方程的利普希茨控制问题研究 |
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| 引用本文： | 黄小玉. 一类二阶常微分方程的利普希茨控制问题研究[J]. 西安石油大学学报(自然科学版), 2011, 26(4): 98-102,12 |
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| 作者姓名： | 黄小玉 |
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| 作者单位： | 广西机电职业技术学院公共教学部,广西南宁,530007 |
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| 摘 要： | 研究了一类由二阶常微分方程所支配的具有状态约束的控制问题.通过状态方程的外部函数来实现系统的控制.在适当的假设条件下,证明了状态方程解的存在惟一性,并证明了当控制函数在利普希茨连续函数类中时,最优控制的存在性.在光滑最优控制情形下,导出了一个最优化必要条件.
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| 关 键 词： | 最优控制 常微分方程 最优化必要条件 |
Lipschitz controls for a class of second-order ordinary differential equations |
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| HUANG Xiao-yu. Lipschitz controls for a class of second-order ordinary differential equations[J]. Journal of Xian Shiyou University, 2011, 26(4): 98-102,12 |
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| Authors: | HUANG Xiao-yu |
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| Affiliation: | HUANG Xiao-yu(Teaching Department of Common Courses,Guangxi Technological College of Machinery and Electricity,Nanning 530007,Guangxi,China) |
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| Abstract: | The control problem with pointwise state constraints governed by a class of second-order ordinary differential equations is studied.The control of the system is realized through the external function of the state equation.Under appropriate assumptions,it is proved that the existence and uniqueness of the solution of the state equation is existing and unique,and it is also proved that optimal control is existing when the control function is Lipschitz continuous function.A necessary optimality condition is de... |
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| Keywords: | optimal control ordinary differential equation optimality necessary condition |
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