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Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics

Abstract : This thesis is devoted to the problem of computing reachable sets of linear and hybrid systems. In the first part, after exposing existing approaches for reachability analysis of linear systems, we present the main contribution of the thesis: a new algorithmic scheme for linear time-invariant systems that definitely outperforms existing algorithms. As the exact implementation furnishes a representation of the reachable sets that is sometimes hard to manipulate, we propose an approximate version that is not subject to the wrapping effect, an uncontrolled growth of the approximation errors. We also discuss a variant of this algorithm specialized to support functions, a functional representation of convex sets. In the second part, we extend this work to hybrid systems. We first show how to deal with the constraints on the continuous dynamics imposed by the invariants. Then, we present algorithms for approximating the intersection of the continuous reachable sets with hyperplanar guards.
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Theses
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https://theses.hal.science/tel-00422569
Contributor : Colas Le Guernic Connect in order to contact the contributor
Submitted on : Wednesday, October 7, 2009 - 3:35:54 PM
Last modification on : Tuesday, October 19, 2021 - 1:47:40 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 12:01:10 PM

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  • HAL Id : tel-00422569, version 1

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Colas Le Guernic. Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics. Computer Science [cs]. Université Joseph-Fourier - Grenoble I, 2009. English. ⟨NNT : ⟩. ⟨tel-00422569v1⟩

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