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3314 Perturbation Approach for Hamilton-Jacobi Equations of Nonlinear Control Systems : II. When all directions near equilibria are unstable
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- HIRATA Yoshihiro
- Ishii Laboratory
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- YAGASAKI Kazuyuki
- Gifu University
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- SAKAMOTO Noboru
- Nagoya University
Bibliographic Information
- Other Title
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- 3314 非線形制御系のハミルトン・ヤコビ方程式に対する摂動論的アプローチ : II.平衡点のまわりのすべての方向が不安定である場合(非線形制御理論とその応用(1))
Description
We analytically study stabilizing solutions to Hamilton-Jacobi equations when all directions near equilibria are unstable, that is, the eigenvalues of the Jacobian matrix at the equilibria are all positive. Applying a perturbation approach, we obtain analytical approximations of stable manifolds in the corresponding Hamiltonian systems, and use their relation to the stabilizing solutions. An illustrative example is given for the two-dimensional Lotka-Volterra system and the theoretical result for the stable manifold is compared with a numerical computation to demonstrate the validity of our method.
Journal
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- The Proceedings of the Symposium on the Motion and Vibration Control
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The Proceedings of the Symposium on the Motion and Vibration Control 2007.10 (0), 434-437, 2007
The Japan Society of Mechanical Engineers
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Keywords
Details 詳細情報について
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- CRID
- 1390282680861647360
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- NII Article ID
- 110007083185
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- ISSN
- 24243000
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- Text Lang
- ja
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- OpenAIRE
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- Abstract License Flag
- Disallowed