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

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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 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.

langue originaleAnglais
titreProceedings of the IEEE Conference on Decision and Control
EditeurInstitute of Electrical and Electronics Engineers Inc.
Pages1071-1076
Nombre de pages6
ISBN (imprimé)9781467357173
Les DOIs
étatPublié - 2013
Evénement52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italie
Durée: 10 déc. 201313 déc. 2013

Une conférence

Une conférence52nd IEEE Conference on Decision and Control, CDC 2013
PaysItalie
La villeFlorence
période10/12/1313/12/13

Empreinte digitale

Spectral Factorization
Boundary Control
Factorization
Optimal Control
Semigroup
Control System
Control systems
Unbounded Operators
Categorical or nominal
Optimal Control Problem
Model
Generator
Abstract Differential Equations
C0-semigroup
Spectral density
Spectral Density
Operator
Affine transformation
Observation
Mathematical operators

Citer ceci

Dehaye, J. R., & Winkin, J. J. (2013). LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation. Dans 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
Dehaye, Jérémy R. ; Winkin, Joseph J. / LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation. Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1071-1076
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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 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.",
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Dehaye, JR & Winkin, JJ 2013, LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation. Dans 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.

Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1071-1076 6760024.

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

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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.

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Dehaye JR, Winkin JJ. LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation. Dans Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc. 2013. p. 1071-1076. 6760024 https://doi.org/10.1109/CDC.2013.6760024