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Modèles et calculs garantis pour les systèmes (min,+)-linéaires

Euriell Le Corronc 1 
1 Modèles et Systèmes Dynamiques
LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
Abstract : This thesis deals with uncertain (min,+)-linear systems contained in intervals, the bounds of which are known. First, as exact computations - sum, inf-convolution, Kleene star/subadditive closure - are often memory consuming and time costly, some approached computations are introduced through inclusion functions. The obtained results are particular intervals called container. The upper bound of a container is the greatest element of the equivalence class of the approached system modulo the Legendre-Fenchel transform. The lower bound of the container is a lower bound of this class, and so of the approached system. The convex characteristics of these bounds provide algorithms of linear or quasi-linear complexity for the computations. Second, the control of uncertain (min,+)-linear systems is studied. These uncertainties can appear after computations realized over the containers introduced above, or when uncertain or variable parameters are present during the modelings. Some existing control structures (precompensator, feedback) are applied over these uncertain systems and the following problems are treated: Window Flow Control problem, reduction of the uncertainty at the output of the system controlled by a precompensator, computation of a neutral precompensator which delays the input without damage the transfer of the system alone.
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Submitted on : Friday, February 3, 2012 - 12:11:05 PM
Last modification on : Wednesday, October 20, 2021 - 3:19:32 AM
Long-term archiving on: : Friday, May 4, 2012 - 2:30:45 AM


  • HAL Id : tel-00665973, version 1


Euriell Le Corronc. Modèles et calculs garantis pour les systèmes (min,+)-linéaires. Automatique. Université d'Angers, 2011. Français. ⟨NNT : ⟩. ⟨tel-00665973⟩



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