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Maxplus algebra and system theory: Where we are and where to go now
 Annu. Rev. Control
, 1999
"... Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison ..."
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Cited by 67 (19 self)
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Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison with classical linear system theory, there are areas which are practically untouched, mostly because the corresponding mathematical tools are yet to be fabricated. This is the case of the geometric approach of systems which is known, in the classical theory, to provide another important insight to systemtheoretic and controlsynthesis problems, beside the algebraic machinery. A preliminary discussion of geometric aspects in the maxplus algebra and their use for system theory is proposed in the last part of the paper. Résumé: Plus de seize ans après le début d’une théorie linéaire de certains systèmes à événements discrets dans laquelle l’algèbre maxplus et autres outils algébriques assimilés jouent un rôle central, ce papier cherche àdécrire quelques uns des principaux résultats obtenus de façon informelle, en s’appuyant sur des exemples. Par comparaison avec la théorie classique des systèmes linéaires, il existe des domaines pratiquement vierges, surtout en raison du fait que les outils mathématiques correspondants restent à forger. C’est en particulier le cas de l’approche géométrique des systèmes qui, dans la théorie classique, est connue pour apporter un autre regard important sur les questions de théorie des systèmes et de synthèse de lois de commandes àcôté de la machinerie purement algébrique. Une discussion préliminaire sur les aspects géométriques de l’algèbre maxplus et leur utilité pour la théorie des systèmes est proposée dans la dernière partie du papier.
Optimal Control of (Min,+) Linear TimeVarying Systems, Petri Nets and Performance Models
 Proceedings of PNPM’99
, 1999
"... The class of discrete event dynamic systems involving only synchronization phenomena can be seen as linear timeinvariant systems in a particular algebraic structure called (�, ) algebra. In the same framework, this paper deals with linear timevarying systems, that is, systems whose parameters may ..."
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The class of discrete event dynamic systems involving only synchronization phenomena can be seen as linear timeinvariant systems in a particular algebraic structure called (�, ) algebra. In the same framework, this paper deals with linear timevarying systems, that is, systems whose parameters may change as functions of time. For example, in a manufacturing system the number of working machines, or the number of trains running in a closed network of railway connections, can vary as functions of time. For such systems, the output tracking problem is optimally solved under justintime criterion. 1.
Adaptive model predictive control for maxpluslinear discrete event inputoutput systems
, 2004
"... ..."
à: Angers
"... Modélisation, analyse de performance et commande des systèmes à événements discrets. ..."
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Modélisation, analyse de performance et commande des systèmes à événements discrets.
23 Heap Models, Composition and Control
"... This chapter deals with modelling and control of discrete event systems. Discrete event systems (DES) are event driven man made systems whose evolution is guided by occurrences of asynchronous events as opposed to classical time driven discrete or continuous systems. DES are modelled by tools from c ..."
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This chapter deals with modelling and control of discrete event systems. Discrete event systems (DES) are event driven man made systems whose evolution is guided by occurrences of asynchronous events as opposed to classical time driven discrete or continuous systems. DES are modelled by tools from computer science like automata, Petri
A Note on the Calculation of a DiscreteEventSystem's Transfer Function
"... In recent research the relevancy of discrete event systems (DES) steadily increases. In order to handle DES the introduction of a DESsystem theory is useful. Hereby the systems are characterised and described by the impulse response and the transfer function. Therefore knowledge about the calcul ..."
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In recent research the relevancy of discrete event systems (DES) steadily increases. In order to handle DES the introduction of a DESsystem theory is useful. Hereby the systems are characterised and described by the impulse response and the transfer function. Therefore knowledge about the calculation and the properties of these functions will be important. This article outlines the DESsystem theory and shows an algorithm for an efficient calculation of the transfer function by means of straightforward algebraic simplifications.