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

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    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