| 引用本文: | 程代展 秦化淑 洪奕光 席在荣.从守恒到开放
——广义哈密顿控制系统的理论和应用*[J].控制理论与应用,1999,16(S1):156~162.[点击复制] |
| Cheng Daizhan Qin Huashu Hong Yiguang Xi Zairong.From Conservation to Openness ——Theory and Applications of Generalized Controlled Hamiltonian Systems[J].Control Theory and Technology,1999,16(S1):156~162.[点击复制] |
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| 从守恒到开放
——广义哈密顿控制系统的理论和应用* |
| From Conservation to Openness ——Theory and Applications of Generalized Controlled Hamiltonian Systems |
| 摘要点击 1328 全文点击 446 |
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| DOI编号 |
| 1999,16(S1):156-162 |
| 中文关键词 广义哈密顿受控系统 Poission流形 辛几何 Casimir函数 励磁控制 |
| 英文关键词 generalized Hamiltonian control systems Poisson manifold Poission manifold symplectic geometry Casimir functions excitation control |
| 基金项目 |
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| 中文摘要 |
| 本文力图从能量的观点处理经典哈密顿控制系统、Poission括号和辛几何.将其推广到具有能量耗散以及与环境有能量交换的广义哈密顿控制系统.提出伪Poission流形与广义辛流形作为一般哈密顿控制系统状态空间的几何框架.讨论了它们的相互关系及一些基本性质.提出广义辛群、辛代数的概念作为广义哈密顿系统的代数结构.基于此研究了广义哈密顿系统的保结构性.然后讨论哈密顿系统的Casimir 流形方法及反馈镇定等问题.得到的结果为进一步研究提供了基础.作为例子，将一些结果应用于电力系统的励磁控制. |
| 英文摘要 |
| The paper intends to treat the classical Hamiltonian systems，Poisson bracket and symplectic geometry from the energy point of view.They are extended to generalized Hamiltonian systems，which have internal dissipation and energy exchange with environment.The pseudo-Poisson manifold and the generalized symplectic manifold are proposes as the geometric frame of the generalized Hamiltonian control systems.The relationship between the pseudo-Poisson manifold and the generalized symplectic manifold and their certain properties are investigated.Then the generalized symplectic group and sympectic algebra are proposed as the algebraic structure of the generalized Hamiltonian systems.The structure-preserving properties of the generalized Hamiltonian systems are investigated.Then the Casimir manifold approach and the feedback stabilization of generalized Hamiltonian systems are discussed.The results obtained provide a foundation for further investigation.As an example，they are applied to the excitation of power systems. |