How to construct an approximate continuous state space for a Petri net system, or whether it is possible to construct an ordinary differential equations (ODEs) for a Petri net system?
Classical Petri nets provide no notion of time, thus (without any extension) a classical continuous state description does not make much sense.
However, if you want to consider PN with time such as time PN (interval PN) or timed PN (duration PN), you get highly non-linear time-dependent systems. To linearize these systems (and to apply something like differential equations) you may transform your state space and apply diodid algebras, see, e.g., the book by Baccelli at al.
There is some work regarding Stochastic Petri Nets. Take a look at DOI 10.1007/978-3-319-07734-5_15 .
You can have a look on the polyhedric techniques used for Petri net with dense time (and also for timed automata) in tools such as Rome (for Petri nets) or UPPAAL (for timed automata).
You can also get some inspiration on interval-based computing (I think IDD - a class of decision diagrams - exploit such features).
These are just my "two cents".
Dear Rahul, you can use Simplorer or Portunus. You have both VHDL-AMS and Petri net modelling.The modelling is graphical in three technical languages: electrical network, information flow scheme and state graphs. All three parts of model are synchronised in the time domain. The computed step size is variable controlled from electrical network part. Nonlinear modelling is suitable with help of imorted measurement data. Simplorer and Portunus are develop for computing, simulation and optimisation of power electronic.
http://simplorer.com/Products/Simulation+Technology/Electronics/Electromechanical/ANSYS+Simplorer
http://www.adapted-solutions.com/Web/ASProduktPortunusUeberblick.html
You can take a look at the fluid Petri nets. If you need more details on the fuild stochastic Petri nets, I can provide more references.
webdiis.unizar.es/~julvez/pub/disca.pdf
www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA306817
http://link.springer.com/chapter/10.1007/978-1-4471-4276-8_18
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