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Pré-Publication, Document De Travail Année : 2008

Control of (max,+)-linear systems minimizing delays

Résumé

In this paper, we study Discrete Events Dynamic Systems (DEDS) that can be modeled by a linear representation on (max,+) algebra. This class corresponds to Timed Event Graphs (TEG). A linear system theory has been developed for these particular systems. Strong analogies then appear between the classical linear system theory and the (max,+)-linear system theory. Some control problems for these systems have previously been tackled. In all these works, the problematic was to compute an optimal solution in regard to the just-in-time criterion, indeed the proposed control laws satisfy some given control objectives while delaying as much as possible occurrences of input or internal events. For our concern, the aim of the control is to delay as less as possible the system while ensuring some given specifications. For example, in a railway network, one can aim at limiting the number of trains in a path while minimizing the induced delays. Another possible application concerns production systems subject to critical time constraints, in which sojourn times of pieces must not exceed a given value at some stages. We may then be interested at bounding the sojourn times while delaying as less as possible the system. We consider two control structures: the control is firstly formalized as a state feedback on state and then as a state feedback on inputs.
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Dates et versions

hal-00345951 , version 1 (10-12-2008)

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  • HAL Id : hal-00345951 , version 1

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Laurent Houssin, Sébastien Lahaye, Jean-Louis Boimond. Control of (max,+)-linear systems minimizing delays. 2008. ⟨hal-00345951⟩
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