Design of Locally Semiconcave Practical Control Lyapunov Function via Multilayer Minimum Projection Method
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- FUKUI Yoshiro
- College of Information Science and Engineering, Ritsumeikan University
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- NAKAMURA Hisakazu
- Faculty of Science and Technology, Tokyo University of Science
Bibliographic Information
- Other Title
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- 多層最小射影法による局所半凹実用制御Lyapunov関数の設計
- タソウ サイショウ シャエイホウ ニ ヨル キョクショ ハンオウジツヨウ セイギョ Lyapunov カンスウ ノ セッケイ
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Abstract
We proposed a Sontag-type feedback controller by using a locally semiconcave practical control Lyapunov function (LS-PCLF) for asymptotic stabilization of a nonlinear system defined on a non-contractible manifold. We also proposed a design method of a nonsmooth control Lyapunov function called the multilayer minimum projection method. However, whether the method can be used as an LS-PCLF design method is not discussed, and we cannot design a controller by using the method and the controller in this situation. In this paper, we study a disassembled differential of a locally semiconcave function to handle an LS-PCLF. The minimal and maximal disassemble differentials, which are special types of a disassembled differential, are introduced. We elucidate that a set of reachable gradients and the Fréchet differential are equivalent to the minimal and maximal disassembled differential, respectively. Based on this fact, we prove that this method can be used as an LS-PCLF design method.
Journal
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- Transactions of the Society of Instrument and Control Engineers
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Transactions of the Society of Instrument and Control Engineers 51 (12), 803-813, 2015
The Society of Instrument and Control Engineers
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Details 詳細情報について
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- CRID
- 1390282679486610176
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- NII Article ID
- 130005114048
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- NII Book ID
- AN00072392
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- ISSN
- 18838189
- 04534654
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- NDL BIB ID
- 027036872
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed