An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory

N. Sakamoto, Arjan van der Schaft

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    1 Citation (Scopus)
    35 Downloads (Pure)

    Abstract

    In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is derived from the theory of 1-st order partial differential equations is considered as an integrable Hamiltonian system with a perturbation caused by control. Assuming that the approximating Riccati equation from the Hamilton-Jacobi equation at the origin has a stabilizing solution, we construct approximating behaviors of the Hamiltonian flows on a stable Lagrangian submanifold, from which an approximation to the stabilizing solution is obtained.
    Original languageUndefined
    Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control
    Place of PublicationUSA
    PublisherIEEE CONTROL SYSTEMS SOCIETY
    Pages5857-5862
    Number of pages6
    ISBN (Print)1-4244-0171-2
    DOIs
    Publication statusPublished - 2006
    Event45th IEEE Conference on Decision and Control, CDC 2006 - San Diego, United States
    Duration: 13 Dec 200615 Dec 2006
    Conference number: 45

    Publication series

    Name
    Number1636734 (P
    ISSN (Print)0191-2216

    Conference

    Conference45th IEEE Conference on Decision and Control, CDC 2006
    Abbreviated titleCDC
    CountryUnited States
    CitySan Diego
    Period13/12/0615/12/06

    Keywords

    • EWI-9202
    • IR-66916
    • METIS-237951

    Cite this

    Sakamoto, N., & van der Schaft, A. (2006). An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory. In Proceedings of the 45th IEEE Conference on Decision and Control (pp. 5857-5862). USA: IEEE CONTROL SYSTEMS SOCIETY. https://doi.org/10.1109/CDC.2006.377789
    Sakamoto, N. ; van der Schaft, Arjan. / An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory. Proceedings of the 45th IEEE Conference on Decision and Control. USA : IEEE CONTROL SYSTEMS SOCIETY, 2006. pp. 5857-5862
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    title = "An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory",
    abstract = "In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is derived from the theory of 1-st order partial differential equations is considered as an integrable Hamiltonian system with a perturbation caused by control. Assuming that the approximating Riccati equation from the Hamilton-Jacobi equation at the origin has a stabilizing solution, we construct approximating behaviors of the Hamiltonian flows on a stable Lagrangian submanifold, from which an approximation to the stabilizing solution is obtained.",
    keywords = "EWI-9202, IR-66916, METIS-237951",
    author = "N. Sakamoto and {van der Schaft}, Arjan",
    note = "De publicatie staat op een CD-rom die voor deze conferentie is uitgegeven.",
    year = "2006",
    doi = "10.1109/CDC.2006.377789",
    language = "Undefined",
    isbn = "1-4244-0171-2",
    publisher = "IEEE CONTROL SYSTEMS SOCIETY",
    number = "1636734 (P",
    pages = "5857--5862",
    booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control",

    }

    Sakamoto, N & van der Schaft, A 2006, An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory. in Proceedings of the 45th IEEE Conference on Decision and Control. IEEE CONTROL SYSTEMS SOCIETY, USA, pp. 5857-5862, 45th IEEE Conference on Decision and Control, CDC 2006, San Diego, United States, 13/12/06. https://doi.org/10.1109/CDC.2006.377789

    An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory. / Sakamoto, N.; van der Schaft, Arjan.

    Proceedings of the 45th IEEE Conference on Decision and Control. USA : IEEE CONTROL SYSTEMS SOCIETY, 2006. p. 5857-5862.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory

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    AU - van der Schaft, Arjan

    N1 - De publicatie staat op een CD-rom die voor deze conferentie is uitgegeven.

    PY - 2006

    Y1 - 2006

    N2 - In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is derived from the theory of 1-st order partial differential equations is considered as an integrable Hamiltonian system with a perturbation caused by control. Assuming that the approximating Riccati equation from the Hamilton-Jacobi equation at the origin has a stabilizing solution, we construct approximating behaviors of the Hamiltonian flows on a stable Lagrangian submanifold, from which an approximation to the stabilizing solution is obtained.

    AB - In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is derived from the theory of 1-st order partial differential equations is considered as an integrable Hamiltonian system with a perturbation caused by control. Assuming that the approximating Riccati equation from the Hamilton-Jacobi equation at the origin has a stabilizing solution, we construct approximating behaviors of the Hamiltonian flows on a stable Lagrangian submanifold, from which an approximation to the stabilizing solution is obtained.

    KW - EWI-9202

    KW - IR-66916

    KW - METIS-237951

    U2 - 10.1109/CDC.2006.377789

    DO - 10.1109/CDC.2006.377789

    M3 - Conference contribution

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    EP - 5862

    BT - Proceedings of the 45th IEEE Conference on Decision and Control

    PB - IEEE CONTROL SYSTEMS SOCIETY

    CY - USA

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    Sakamoto N, van der Schaft A. An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory. In Proceedings of the 45th IEEE Conference on Decision and Control. USA: IEEE CONTROL SYSTEMS SOCIETY. 2006. p. 5857-5862 https://doi.org/10.1109/CDC.2006.377789