NDLI: Modeling and Control of Weight-Balanced Timed Event Graphs in Dioids

Content Provider	IEEE Xplore Digital Library
Author	Cottenceau, B. Hardouin, L. Boimond, J.-L.
Copyright Year	1963
Abstract	The class of timed event graphs (TEGs) has widely been studied thanks to an approach known as the theory of max-plus linear systems. In particular, the modeling of TEGs via formal power series in a dioid called Min^ax [[ γ,δ]] has led to input-output representations on which some model matching control problems have been solved. Our work attempts to extend the class of systems for which a similar control synthesis is possible. To this end, a subclass of timed Petri nets that we call weight-balanced timed event graphs (WBTEGs) will be first defined. They can model synchronization and delays (WBTEGs contain TEGs) and can also describe dynamic phenomena such as batching and event duplications (unbatching). Their behavior is described by rational compositions (sum, product and Kleene star) of four elementary operators γⁿ, δ^t, μm, and βb on a dioid of formal power series denoted ε* [[ δ]]. The main feature is that the transfer series of WBTEGs have a property of ultimate periodicity (such as rational series in M_in^ax [[ γ,δ]]). Finally, the existing results on control synthesis for max-plus linear systems find a natural application in this framework.
Sponsorship	IEEE Control Systems Society
Starting Page	1219
Ending Page	1231
Page Count	13
File Size	5359825
File Format	PDF
ISSN	00189286
Volume Number	59
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Radiation detectors Additives Computational modeling Synchronization Calculus Petri nets Silicon weighted timed event graphs (WTEGs) Controller synthesis dioids discrete-event systems formal power series residuation
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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