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Virtual Lagrangian Construction Method for Infinite-Dimensional Systems with Homotopy Operators

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Lagrangian and Hamiltonian Methods for Nonlinear Control 2006

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 366))

Abstract

This paper presents a general modeling method to construct a virtual Lagrangian for infinite-dimensional systems. If the system is self-adjoint in the sense of the Fretchet derivative, there exists some Lagrangian for a stationary condition of variational problems. A system having such a Lagrangian can be formulated as a field port-Lagrangian system by using a Stokes-Dirac structure on a variational complex. However, it is unknown whether any infinite-dimensional system can be expressed as an Euler-Lagrange equation. Then, we introduce a virtual Lagrangian with a homotopy operator. The virtual Lagrangian defines a self-adjoint subsystem, which is realized by a cancellation of non-self-adjoint error subsystems.

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Author information

Authors and Affiliations

  1. Environment Adaptive Robotic Systems Lab., Bio-Mimetic Control Research Center, RIKEN (The Institute of Physical and Chemical Research), 2271-130 Anagahora, Shimoshidami, Moriyama-ku, Nagoya, Aichi, 463-0003, Japan

    Gou Nishida

  2. Department of Mechanical and Control Engineering, Tokyo Institute of Technology/RIKEN BMC, 2-12-1 Ohokayama, Meguro-ku, Tokyo, 152-8552, Japan

    Masaki Yamakita

  3. Department of Computer and Systems Engineering, Kobe University/RIKEN BMC, 1-1 Rokkodai, Nada-ku, Kobe, Hyogo, 657-8501, Japan

    Zhiwei Luo

Authors
  1. Gou Nishida
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  2. Masaki Yamakita
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  3. Zhiwei Luo
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Editor information

Editors and Affiliations

  1. Mechanical Engineering Department, University of California at Santa Barbara, 2338 Engineering Bldg II, Santa Barbara, CA, 93106-5070, USA

    Francesco Bullo

  2. Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

    Kenji Fujimoto

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© 2007 Springer-Verlag Berlin Heidelberg

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Nishida, G., Yamakita, M., Luo, Z. (2007). Virtual Lagrangian Construction Method for Infinite-Dimensional Systems with Homotopy Operators. In: Allgüwer, F., et al. Lagrangian and Hamiltonian Methods for Nonlinear Control 2006. Lecture Notes in Control and Information Sciences, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73890-9_5

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  • DOI: https://doi.org/10.1007/978-3-540-73890-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73889-3

  • Online ISBN: 978-3-540-73890-9

  • eBook Packages: EngineeringEngineering (R0)

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