### Résumé

A model of boundary control system with boundary observation is described and analyzed, which involves no unbounded operator except for the dynamics generator. The resolution of a LQ-optimal control problem for this model provides a stabilizing feedback for a nominal system with unbounded operators. The model consists of an extended abstract differential equation whose state components are the boundary input, the state (up to an affine transformation) and a Yosida-type approximation of the output of the nominal system. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of an analytic C_{0}- semigroup and the model is observable. A LQ-optimal control problem is posed for the model, and a general method of resolution based on the problem of spectral factorization of a multi-dimensional operator-valued spectral density is described. It is expected that this approach will lead hopefully to a good trade-off between the cost of modelling and the efficiency of methods of resolution of control problems for such systems.

langue originale | Anglais |
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titre | Proceedings of the IEEE Conference on Decision and Control |

Editeur | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1071-1076 |

Nombre de pages | 6 |

ISBN (imprimé) | 9781467357173 |

Les DOIs | |

état | Publié - 2013 |

Evénement | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italie Durée: 10 déc. 2013 → 13 déc. 2013 |

### Une conférence

Une conférence | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Pays | Italie |

La ville | Florence |

période | 10/12/13 → 13/12/13 |

### Empreinte digitale

### Citer ceci

*Proceedings of the IEEE Conference on Decision and Control*(p. 1071-1076). [6760024] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760024

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*Proceedings of the IEEE Conference on Decision and Control.*, 6760024, Institute of Electrical and Electronics Engineers Inc., p. 1071-1076, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italie, 10/12/13. https://doi.org/10.1109/CDC.2013.6760024

**LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation.** / Dehaye, Jérémy R.; Winkin, Joseph J.

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Article dans les actes d'une conférence/un colloque

TY - GEN

T1 - LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation

AU - Dehaye, Jérémy R.

AU - Winkin, Joseph J.

PY - 2013

Y1 - 2013

N2 - A model of boundary control system with boundary observation is described and analyzed, which involves no unbounded operator except for the dynamics generator. The resolution of a LQ-optimal control problem for this model provides a stabilizing feedback for a nominal system with unbounded operators. The model consists of an extended abstract differential equation whose state components are the boundary input, the state (up to an affine transformation) and a Yosida-type approximation of the output of the nominal system. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of an analytic C0- semigroup and the model is observable. A LQ-optimal control problem is posed for the model, and a general method of resolution based on the problem of spectral factorization of a multi-dimensional operator-valued spectral density is described. It is expected that this approach will lead hopefully to a good trade-off between the cost of modelling and the efficiency of methods of resolution of control problems for such systems.

AB - A model of boundary control system with boundary observation is described and analyzed, which involves no unbounded operator except for the dynamics generator. The resolution of a LQ-optimal control problem for this model provides a stabilizing feedback for a nominal system with unbounded operators. The model consists of an extended abstract differential equation whose state components are the boundary input, the state (up to an affine transformation) and a Yosida-type approximation of the output of the nominal system. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of an analytic C0- semigroup and the model is observable. A LQ-optimal control problem is posed for the model, and a general method of resolution based on the problem of spectral factorization of a multi-dimensional operator-valued spectral density is described. It is expected that this approach will lead hopefully to a good trade-off between the cost of modelling and the efficiency of methods of resolution of control problems for such systems.

UR - http://www.scopus.com/inward/record.url?scp=84902338965&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760024

DO - 10.1109/CDC.2013.6760024

M3 - Conference contribution

SN - 9781467357173

SP - 1071

EP - 1076

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Institute of Electrical and Electronics Engineers Inc.

ER -