NDLI: Static nonsmooth control Lyapunov function design via dynamic extension

Content Provider	IEEE Xplore Digital Library
Author	Yamazaki, T. Yamashita, Y. Nakamura, H.
Copyright Year	2011
Description	Author affiliation: Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510, Japan (Nakamura, H.) \|\| Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14W8, Sapporo 060-0814, Japan (Yamazaki, T.; Yamashita, Y.)
Abstract	In this paper, we propose a method to obtain a control Lyapunov function (CLF) by the reduction of a CLF of an augmented system with a dynamic compensator. For asymptotically stabilizing control, dynamic compensators are not necessary in most of the cases. However, in some cases, we can easily design a stabilizing control law using a dynamic compensator. Therefore, a constructive design method using a static controller via a dynamic controller has advantages and is preferable in practice. In this paper, we assume that a CLF has been designed on an extended state space with a dynamic compensator, and show that taking minimum values of the CLF on the extended state space gives a nonsmooth CLF on the original state space. This method can be considered as an extension of the minimum projection method[1], [2]. We also show that the obtained CLF fulfills Lipschitz continuity and local semiconcavity if the original CLF on the extended state space is Lipschitz continuous and locally semiconcave. The effectiveness of the proposed method is demonstrated by an example.
Starting Page	7573
Ending Page	7578
File Size	255979
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6161012
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Aerospace electronics Manifolds Nonlinear dynamical systems Lyapunov methods Vectors Educational institutions Differential equations
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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