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)
32 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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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.",
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year = "2006",
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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

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

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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.

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KW - IR-66916

KW - METIS-237951

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

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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