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# An algorithm for the evolution graph of extended Hybrid Petri nets

An algorithm for the evolution graph of extended Hybrid Petri nets

## An algorithm for the evolution graph of extended Hybrid Petri

An algorithm for the evolution graph of extended HybridPetri nets *Martina SvadovaCenter for Applied CyberneticsCzech Technical UniversityPrague 2, Czech Republicxsvadova@control.felk.cvut.czAbstract - Extended Hybrid Petri nets (eHPNs) definedby David & Caramihai are one of possible extensions ofHybrid Petri nets modeling a delay on continuous flow.The behavior of hybrid dynamic systems, modeled byeHPNs, can be studied using an evolution graph. Thispaper introduces an algorithm generating the evolutiongraph consisting of IB-states. A model of hydro-system isused as an illustrative example.Keywords: Delay, Extended Hybrid Petri nets, Evolutiongraph algotihm1 IntroductionPetri nets (PNs) [1],[6] are generally used to modeland analyze discrete event dynamic systems likemanufacturing systems and communication protocols.Hybrid systems consisting of discrete and continuousparts can be modeled by Hybrid Petri nets [2],[5].First-Order HPNs (FOHPNs) were studied in [7] byBalduzzi, Guia and Seatzu. In contrast to classical HPNsdefined by David & Alla this type of PNs has two maindifferences in continuous part. First, in FOHPNcontinuous transitions are always strongly enabled.Second, instantaneous firing speed can be constrained byminimum firing speeds in FOHPN.Neither the classical Hybrid Petri nets [5] nor theFOHPN do not allow to model the systems with delay oncontinuous flow (e.g. the product delay on the conveyor,the delay of fluid in pipe). Extended Hybrid Petri nets(eHPNs) defined by David & Caramihai [3] are one ofpossible extensions of Hybrid Petri nets modeling delayon continuous flow. This article aims at algorithmisationof this model.Behavior of deterministic hybrid dynamic systems,modeled by eHPNs, can be analyzed by an evolutiongraph, which is composed from so-called invariantbehavior states (IB-state) and transitions betweenparticular IB-states.Zdenek HanzalekCenter for Applied Cybernetics,Czech Technical UniversityPrague 2, Czech Republichanzalek@control.felk.cvut.czThis paper describes an algorithm generating anevolution graph consisting of IB-states characterized byconstant marking of discrete places, by constantinstantaneous firing speed of continuous transitions.Further the IB-state is characterized at its entry point bythe continuous marking and by the elapsed time of eachenabled discrete transition. The transitions between IBstatesare characterized by the event provoking thetransition and by the elapsed time in previous IB-state.The algorithm is part of the PN Matlab Toolbox [4].The paper is organized as follows: Section 2 brieflypresents eHPNs. Section 3 describes the algorithm forgenerating of the eHPNs. Section 4 presents an exampleshowing functionality of the presented algorithm. Amodel of a hydro-system is used as illustrative example.2 Extended Hybrid Petri netsBasic notion of an extended Hybrid Petri nets(eHPNs) is defined in this section. The extended HybridPetri nets defined by David & Caramihai [3] allow tomodel systems with delays on the continuous flow. Theyare extension of classical Hybrid Petri nets defined byAlla & David [2] and they assume all their properties.A marked timed eHPN is defined by the seven-tuple: (1)P = P ∪ CPT = T ∪ CT∪ eTfinite and non-empty set ofplaces, (P - the set of discreteplaces and CP - the set ofcontinuous places (P and CP aredisjoint)finite and non-empty set oftransitions, where T is the set ofdiscrete transitions; eT is theset of extended transitions andCT is the set of continuoustransitions (T, CT and eT aredisjoint)* 0-7803-8566-7/04/\$20.00 © 2004 IEEE.

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