| EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS |
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| 引用本文： | Yuqian GUO Daizhan CHENG. EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS[J]. 系统科学与复杂性, 2006, 19(2): 211-218. DOI: 10.1007/s11424-006-0211-4 |
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| 作者姓名： | Yuqian GUO Daizhan CHENG |
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| 作者单位： | Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grants 60221301 and 60334040. |
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| 摘 要： | In this paper,we first propose an extended Casimir method for energy-shaping.Then itis used to solve some control problems of Hamiltonian systems.To solve the H_x control problem,theenergy function of a Hamiltonian system is shaped to such a form that could be a candidate solution ofHJI inequality.Next,the energy function is shaped as a candidate of control ISS-Lyapunov function,and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved.Someeasily verifiable sufficient conditions are presented.
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| 关 键 词： | H∞控制 稳定性 汉密尔顿函数 Casimir函数 |
| 收稿时间： | 2005-09-08 |
| 修稿时间： | 2005-09-082006-02-27 |
Extended Casimir Approach to Controlled Hamiltonian Systems |
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| Yuqian Guo,Daizhan Cheng. Extended Casimir Approach to Controlled Hamiltonian Systems[J]. Journal of Systems Science and Complexity, 2006, 19(2): 211-218. DOI: 10.1007/s11424-006-0211-4 |
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| Authors: | Yuqian Guo Daizhan Cheng |
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| Affiliation: | (1) Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the Hoo control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented. |
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| Keywords: | Casimir function Energy-shaping H∞ control Input-to-state stabilization |
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