### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1071-1076 |

Number of pages | 6 |

ISBN (Print) | 9781467357173 |

DOIs | |

Publication status | Published - 2013 |

Event | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: 10 Dec 2013 → 13 Dec 2013 |

### Conference

Conference | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Country | Italy |

City | Florence |

Period | 10/12/13 → 13/12/13 |

### Fingerprint

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 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., pp. 1071-1076, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 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.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

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

AN - SCOPUS:84902338965

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 -