Kaliczyńska Małgorzata - Automation 2017: innovations in automations, robotics and measurement techniques

Institute of Informatics, Slovak Academy of Sciences, Dbravsk cesta 9, 845 07 Bratislava, Slovak Republic

Frantiek apkovi

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URL: http://www.ui.sav.sk/home/capkovic/capkhome.htm

Place/transition PN (P/T PN) [] of FMS. As to their structure P/T PN are bipartite directed graphs . The nodes are represented by places , and transitions . Two kinds of edges (from places to transitions and the edges from transitions to places) are given, respectively, in the form of the sets and . Next to the structure, P/T PN have also their dynamics which can formally be expressed as . Here, X is the set of the state vectors of the places ( symbolizes integers), U is the set of the state vectors of the transitions, is a transition function yielding the new state (marking) vector based on both an existing state and an occurrence of discrete events . Dynamics, being the evolution of marking of the P/T PN places, is given by the linear discrete model restricted by the inequality , . Here, with (i.e. , where symbolizes natural numbers), is the marking vector expressing the state of the marking of the particular places (the number of tokens inside the places) and with is the vector of the states of transitions (either disabled or enabled). The matrix , , expresses the PN structure. ( ), (here symbolizes non-negative integers) and ( ) are the incidence matrices of the arcs corresponding, respectively, to the sets F and G .

The places model activities (operations) in FMS, while the transitions model the discrete events (starting/ending the activities). P/T PN do not depend on time. Their transitions, places, arcs and tokens do not contain any time specifications.