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Communication Dans Un Congrès Année : 2022

Systems synchronisation in Max-Plus algebra: a controlled invariance perspective - In memoriam Édouard Wagneur

Résumé

We study the concept of systems synchronisation in Max-Plus algebra. We show that the problem of synchronising Max-Plus linear systems is twofold. It can be stated in terms of controlled invariance, and of coreachability. The controlled invariance is the property of a set for which a suitable control exists, that maintains the trajectory in the set. We recall some properties of controlled invariance, in particular the existence of a maximal controlled invariant set included into any given set. Beyond the determination of the admissible controlled invariant set, we define and study a problem of coreachability. The controlled invariant set is the target and we study the existence of a control law that brings the trajectory to the target from the initial state within a specific number of steps. We illustrate the study with an example from the literature.
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Dates et versions

hal-03856105 , version 1 (16-11-2022)

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  • HAL Id : hal-03856105 , version 1

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Claude Martinez, Redouane Kara, J.-J. Loiseau. Systems synchronisation in Max-Plus algebra: a controlled invariance perspective - In memoriam Édouard Wagneur. IFAC Workshop on Complex Systems (COSY 2022), Nov 2022, Bologna, Italy. ⟨hal-03856105⟩
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