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    Soutenance de thèse de Monsieur Renato Markele FERREIRA CÂNDIDO

    Soutenance de thèse de Monsieur Renato Markele FERREIRA CÂNDIDO

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    Soutenance de thèse de Monsieur Renato Markele FERREIRA CÂNDIDO

    14h00 | The State University of Campinas | BRÉSIL

    Le 23 juin 2017

    Sujet : Reachability Analysis of Uncertain Max Plus Linear Systems

    Directeur de thèse : Monsieur Laurent HARDOUIN

    RÉSUMÉ

    Discrete Event Dynamic Systems (DEDS) are discrete-state systems whose dynamics are entirely driven by the occurrence of asynchronous events over time. Linear equations in the max-plus algebra can be used to describe DEDS subjected to synchronization and time delay phenomena. The reachability analysis concerns the computation of all states that can be reached by a dynamical system from an initial set of states. The reachability analysis problem of Max Plus Linear (MPL) systems has been properly solved by characterizing the MPL systems as a combination of Piece-Wise Affine (PWA) systems and then representing each component of the PWA system as Difference-Bound Matrices (DBM). The main contribution of this thesis is to present a similar procedure to solve the reachability analysis problem of MPL systems subjected to bounded noise, disturbances and/or modeling errors, called uncertain MPL (uMPL) systems. First, we present a procedure to partition the state space of an uMPL system into components that can be completely represented by DBM. Then we extend the reachability analysis of MPL systems to uMPL systems. Moreover, the results on reachability analysis of uMPL systems are used to solve the conditional reachability problem, which is closely related to the support calculation of the probability density function involved in the stochastic filtering problem.