On fluidization of discrete event models: observation and control of continuous Petri nets

Abstract

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

An information theoretic approach for knowledge representation using Petri nets

“…Traditionally, tokens in classical PNs are interpreted as moving objects (typically integer units) in a network of interconnected places, as mentioned in Section I-A. Further approaches encountered in the literature consider different kind of tokens, like for example numerical tokens [5], [6], fuzzy tokens [4], [7], particle tokens [8], [9], to cite just but any, each one providing some changes on the net dynamics, yet defining a variant of the classical PNs.…”

Applying Petri nets to modeling the chemical stage of radiobiological mechanism

“…Great advantage of Petri nets for modeling complicated distributed systems consists then in the possibility of being easily created with the help of graphical tools and of rapid analysis of the corresponding system which enables us to optimize the parameters of a mathematical model (see e.g. [13,14,22,23]). Unlike the classical methods creating mathematical models with the help of programing languages the Petri nets enable us to form gradually a mathematical model via places and transitions.…”

Minimum-time decentralized control of Choice-Free continuous Petri nets

“…For the kind of timed CPN under infinite server semantics, several control approaches have been considered. In [2], the optimal steady state control problem is studied. Model Predictive Control is used for optimal control problem in [7] assuming a discrete-time model.…”

“…Continuous PN (CPN) [1,2] are fluid approximations of classical discrete PN obtained by removing the integrality constraints, which means that the firing count vector and consequently the marking are no longer restricted to be in the naturals but relaxed into the non-negative real numbers. An important advantage of this relaxation is that more efficient algorithms are available for their analysis.…”