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| HAL : hal-00013870, version 1 |
| Fiche détaillée |  Récupérer au format |
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| SIAM Journal on Control and Optimization 44 no 1 (2005) 349--366 |
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| A spillover phenomenon in the optimal location of actuators |
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| Pascal Hebrard 1, 2Antoine Henrot 1, 2 |
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| (2005) |
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| In this paper, we are interested in finding the optimal location and shape of the actuators in a stabilization problem. Namely, we consider the one-dimensional wave equation damped by an internal feedback supported on a subdomain $\omega$ of given length. The criterion we want to optimize represents the rate of decay of the total energy of the system. It theoretically involves all the eigenmodes of the operator. From an engineering point of view, it seems more realistic to consider only a finite number of modes, say the $N$ first ones. In that context, we are able to prove existence and uniqueness of an optimal domain $\omega_N^*$: it is the better possible location for the actuators. We characterize this optimal domain and we point out the following strange phenomenon (at least for small lengths): the optimal domain $\omega_N^*$ which is the better one for the $N$ first modes is actually the worse one for the $N+1$-th mode. This looks like to the well-known spillover phenomenon in Control Theory. At last, we will give some possible extension and open problems in higher dimension. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| 2 : | CORIDA (INRIA Lorraine / IECN / MMAS) |
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INRIA – CNRS : UMR7122 – CNRS : UMR7502 – Université Paul Verlaine - Metz – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| Equations aux Dérivées Partielles |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| damped wave equation – optimal location – spillover – stabilization |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00013870, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00013870 | |
| oai:hal.archives-ouvertes.fr:hal-00013870 | |
| Contributeur : Antoine Henrot | |
| Soumis le : Mardi 15 Novembre 2005, 08:13:48 | |
| Dernière modification le : Jeudi 14 Septembre 2006, 17:11:34 | |
