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

Sakamoto, N. and Schaft van der, A.J. (2006) *An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory.* In: 45th IEEE Conference on Decision and Control, 13-15 Dec 2006, San Diego, CA, USA.

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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. |

Item Type: | Conference or Workshop Item |

Copyright: | © 2006 IEEE |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/66916 |

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