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Theses

Techniques pour l'analyse formelle de systèmes dynamiques non-linéaires

Abstract : In this thesis, we presented our contributions to the formal analysis of dynamical systems. We focused on the problem of efficiently computing an accurate approximation of the reachable sets under nonlinear dynamics given by differential equations. Our aim was also to design scalable methods which can handle large systems. The first contribution of this thesis concerns the dynamic hybridization technique for a large class of nonlinear systems. We focused on the hybridization domain construction such that the linear interpolation realized in this domain ensures a desired error between the original system trajectories and those computed with the approximated system. We propose a construction method which tends to maximize the domain volume which reduce the number of creation of new domains during the analysis. The second research direction that we followed concerns a subclass of nonlinear dynamical systems which are the polynomial systems. Our results for the reachability analysis of these systems are based on the Bernstein expansion properties. We approximate an initial reachability computation (which requires solving polynomial optimization problems) with an accurate over-approximation (which requires solving linear optimization problems). The last theoretical contribution concerns the reachability analysis of linear systems with polyhedral input which often result from approximation of nonlinear systems. We proposed a technique to refine
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Romain Testylier. Techniques pour l'analyse formelle de systèmes dynamiques non-linéaires. Autre [cs.OH]. Université de Grenoble, 2012. Français. ⟨NNT : 2012GRENM097⟩. ⟨tel-00910330⟩

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