**Conference Paper:**L2 optimal model reduction

Title | L2 optimal model reduction |
---|---|

Authors | Yan, WeiYong1 Lam, James1 |

Keywords | Technology: comprehensive works |

Issue Date | 1996 |

Publisher | IEEE. The Journal's web site is located at http://www.ieeecss.org |

Citation | Proceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281 [How to Cite?] DOI: http://dx.doi.org/10.1109/CDC.1996.577460 |

Abstract | This paper deals with the problem of computing an L2-optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the L2 model reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form formula for the gradient of the cost over the manifold is derived, from which a gradient flow is formed as an ordinary differential equation. A number of nice properties about such a flow are obtained. Among them are the decreasing property of the cost along the ODE solution and the convergence of the flow from any starting point in the manifold. Furthermore, an explicit iterative convergent algorithm is developed from the flow and inherits the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model-reduction cost is decreasing to minimums along the iterates. |

ISSN | 0191-2216 2012 SCImago Journal Rankings: 0.746 |

DOI | http://dx.doi.org/10.1109/CDC.1996.577460 |

DC Field | Value |
---|---|

dc.contributor.author | Yan, WeiYong |

dc.contributor.author | Lam, James |

dc.date.accessioned | 2007-10-30T06:54:27Z |

dc.date.available | 2007-10-30T06:54:27Z |

dc.date.issued | 1996 |

dc.description.abstract | This paper deals with the problem of computing an L2-optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the L2 model reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form formula for the gradient of the cost over the manifold is derived, from which a gradient flow is formed as an ordinary differential equation. A number of nice properties about such a flow are obtained. Among them are the decreasing property of the cost along the ODE solution and the convergence of the flow from any starting point in the manifold. Furthermore, an explicit iterative convergent algorithm is developed from the flow and inherits the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model-reduction cost is decreasing to minimums along the iterates. |

dc.description.nature | published_or_final_version |

dc.format.extent | 557762 bytes |

dc.format.extent | 10566 bytes |

dc.format.mimetype | application/pdf |

dc.format.mimetype | text/plain |

dc.identifier.citation | Proceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281 [How to Cite?] DOI: http://dx.doi.org/10.1109/CDC.1996.577460 |

dc.identifier.doi | http://dx.doi.org/10.1109/CDC.1996.577460 |

dc.identifier.epage | 4281 |

dc.identifier.hkuros | 25686 |

dc.identifier.issn | 0191-2216 2012 SCImago Journal Rankings: 0.746 |

dc.identifier.openurl | |

dc.identifier.scopus | eid_2-s2.0-0030385488 |

dc.identifier.spage | 4276 |

dc.identifier.uri | http://hdl.handle.net/10722/46622 |

dc.identifier.volume | 4 |

dc.language | eng |

dc.publisher | IEEE. The Journal's web site is located at http://www.ieeecss.org |

dc.relation.ispartof | Proceedings of the IEEE Conference on Decision and Control |

dc.rights | ©1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. |

dc.rights | Creative Commons: Attribution 3.0 Hong Kong License |

dc.subject | Technology: comprehensive works |

dc.title | L2 optimal model reduction |

dc.type | Conference_Paper |

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Author Affiliations

- Nanyang Technological University