### Abstract

Original language | Undefined |
---|---|

Title of host publication | Proceedings of the 45th IEEE Conference on Decision and Control |

Place of Publication | USA |

Publisher | IEEE CONTROL SYSTEMS SOCIETY |

Pages | 5857-5862 |

Number of pages | 6 |

ISBN (Print) | 1-4244-0171-2 |

DOIs | |

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 | |
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Number | 1636734 (P |

ISSN (Print) | 0191-2216 |

### Conference

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

Abbreviated title | CDC |

Country | United States |

City | San Diego |

Period | 13/12/06 → 15/12/06 |

### Keywords

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

### Cite this

*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

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*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.

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 - 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

SN - 1-4244-0171-2

SP - 5857

EP - 5862

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

PB - IEEE CONTROL SYSTEMS SOCIETY

CY - USA

ER -