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An Algorithm to Compute the Inverse Image of a Point with Respect to a Nondeterministic Max Plus Linear System

Abstract : Max Plus Linear (MPL) systems are often described by a transition function, which models the state evolution of the system, and a measurement function, which binds the measures with the system states. Methods for computing the inverse image of a point w.r.t. the measurement function are particularly interesting in applications where it is desirable to obtain informations about the system states based on the output observations. The inverse image of a set w.r.t. a nondeterministic MPL system, called uncertain MPL (uMPL) system, can be computed by using the Difference-Bound Matrices (DBM) approach. In this work we aim to use an interval analysis to propose a method to compute the inverse image of a point w.r.t. an uMPL system. The algorithm proposed has a lower worst-case complexity compared with the DBM approach as previously proposed in the literature.
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https://hal.univ-angers.fr/hal-02961770
Contributeur : Laurent Hardouin <>
Soumis le : jeudi 8 octobre 2020 - 16:40:03
Dernière modification le : mercredi 14 octobre 2020 - 03:04:40

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Renato Markele Ferreira Cândido, Laurent Hardouin, Mehdi Lhommeau, Rafael Santos-Mendes. An Algorithm to Compute the Inverse Image of a Point with Respect to a Nondeterministic Max Plus Linear System. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2020, pp.1-1. ⟨10.1109/TAC.2020.2998726⟩. ⟨hal-02961770⟩

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