| 引用本文: | 赵怡,刘明扬.关于一类双线性系统能达性及最优控制问题*[J].控制理论与应用,1987,4(4):9~16.[点击复制] |
| Zhao Yi, Liu Mingyang.A DISCUSSION ON THE ATTAINABILITY PROBLEMS FOR A CLASS OF BILINEAR SYSTEMS*[J].Control Theory and Technology,1987,4(4):9~16.[点击复制] |
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| 关于一类双线性系统能达性及最优控制问题* |
| A DISCUSSION ON THE ATTAINABILITY PROBLEMS FOR A CLASS OF BILINEAR SYSTEMS* |
| 摘要点击 1114 全文点击 500 投稿时间：1984-12-08 修订日期：1987-07-22 |
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| DOI编号 |
| 1987,4(4):9-16 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 本文在某些空间结构下讨论了如下的双线性控制系统
x’(t) + A(t)x(t) = u(t)B(t)x(t) + f(t),
x(0) = x0. t∈(0, T)
在关于算子A(t)及B(t)的某些假设下，给出了系统的分布解及轨道集合的性质。通过引入共轭系统及应用半群理论给出了系统的某些逼近能达性及布局能达性的结果，并应用上结果讨论述了某些类型的最优控制问题。 |
| 英文摘要 |
| In this paper, we consider the following bilinear control system
x’(t) + A(t)x(t) = u(t)B(t)x(t) + f(t),
x(0) = x0. t∈(0, T)
under some space structures.
This properties of the distributed solution and the set of the trajectories of the system are given under certain assumptions on operators A(t) and B(t). Results concerning the approximate and locally approximate reachability are presented by introducing conjugate system and using semigroup theory. Some specific optimal control problems are discussed by virtue of foregoing results. |
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