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

doi:10.1109/CDC.2006.377789

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 proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

167 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 language	Undefined
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control
Place of Publication	USA
Publisher	IEEE
Pages	5857-5862
Number of pages	6
ISBN (Print)	1-4244-0171-2
DOIs	https://doi.org/10.1109/CDC.2006.377789
Publication status	Published - 2006
Event	45th IEEE Conference on Decision and Control, CDC 2006 - San Diego, United States Duration: 13 Dec 2006 → 15 Dec 2006 Conference number: 45

Publication series

Name
Number	1636734 (P
ISSN (Print)	0191-2216

Conference

Conference	45th IEEE Conference on Decision and Control, CDC 2006
Abbreviated title	CDC
Country/Territory	United States
City	San Diego
Period	13/12/06 → 15/12/06

Keywords

EWI-9202
IR-66916
METIS-237951

Access to Document

10.1109/CDC.2006.377789

Cite this

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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.; 45th IEEE Conference on Decision and Control, CDC 2006 ; Conference date: 13-12-2006 Through 15-12-2006",

year = "2006",

doi = "10.1109/CDC.2006.377789",

language = "Undefined",

isbn = "1-4244-0171-2",

publisher = "IEEE",

number = "1636734 (P",

pages = "5857--5862",

booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control",

address = "United States",

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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, USA, pp. 5857-5862, 45th IEEE Conference on Decision and Control, CDC 2006, San Diego, California, 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, 2006. p. 5857-5862.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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

AU - Sakamoto, N.

AU - van der Schaft, Arjan

N1 - Conference code: 45

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

SN - 1-4244-0171-2

SP - 5857

EP - 5862

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

PB - IEEE

CY - USA

T2 - 45th IEEE Conference on Decision and Control, CDC 2006

Y2 - 13 December 2006 through 15 December 2006

ER -