A. Contours-de-bromwich-optimisés and .. , 121 A.4.1 Estimations d'erreur, p.123

. En, algorithmes mettant en oeuvre la méthode des séries de Fourier ontétéontété développés, permettant une approche de la transformée de Laplace inverse par une série de Fourier infinie Koizumi [47] publie le premier article utilisant une telle procédure numérique. Parmi les plus populaires procédures qui ont suivi, on cite Dubner-Abate, Hosono Honig-Hirdes (1984) et Piessens-Huysmans, p.Crump, 1935.

. Enfin, utilisant la déformation du contour dans l'intégrale de Bromwich, figure parmi les meilleures approches pour calculer la transformée de Laplace inverse. L'article de référence de cette approche a ´ eté publié par Talbot, 1979.

Q. Dans-ce and . Suit, onétudieonétudie plusieurs algorithmes utilisant cette approche. On portera une attentionparticulì erè a la méthode proposant l

. Cependant, optimalité des paramètres n'a pasétépasété formellementétablieformellementétablie De plus, les résultats sont " optimaux " pour un temps t donné et aucune preuve de leur efficacité pour les autres temps n'a ´ eté apportée

.. En-espace, 130 B.1.2 Approche semi-décentralisée via unprobì eme inverse du contrôle optimal distribué, Sommaire B.1 Systèmes Distribués Invariant, p.131

. Dans-ce-cas, il existe un contrôle u(t, ?) invariant par translation du système (B.1) qui minimise (B.3), voir, Ce contrôle optimal de (B.1) peutêtrepeutêtre facilement obtenu en appliquant la transformée de Fourier inversè a

. En-général, est une fonction irrationnelle de ?. Ainsi, le contrôleur ne peut pasêtrepasêtre mis en oeuvre par uné equation aux dérivées partielles (EDP) en t et ?

. Dans, la décroissance exponentielle rapide en espace de K a ´ etéetéétablie Cela signifie que le contrôleur optimal résultant a un degré de localisation spatiale et peut doncêtredoncêtre mis en oeuvre d'une façon distribuée

. Dans, auteur propose une stratégie pour la conception de contrôleurs optimaux semi-décentralisés, détaillée dans la section suivante

G. Choudhury and W. Whitt, 1) est invariant en espaceauteur propose unprobì eme inverse optimal de stabilisation exponentielle associéassociéà (B.1) Ceprobì eme est dit inverse dans le sens o` u le contrôle qui stabilise le système (B.1), minimise une fonctionnelle de coût choisie a posteriori Autrement dit, les opérateurs Q et R dans la fonctionnelle (B.3) ne sont pas a priori fixés. Ils sont plutôt choisis a posteriori par la stabilisation exponentielle de l'´ etat-feedback. Concernant l'optimalité On the laguerre-method for numerically inverting laplace transforms, Dans cette section, on suppose que le système, pp.413-427, 1996.

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