Hassane Alla

Continuous and hybrid Petri nets

Petri nets are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems…). When a PN contains a large number of tokens, the number of reachable states explodes. This is a practical limitation to the use of Petri nets. Continuous models may provide very good approximations for discrete event systems: this is the basic idea leading to the definition of continuous Petri nets. A continuous PN is a model in which the marking of each place is a real number. In a timed continuous PN, a firing speed is associated with each transition (this basic model is unique although the firing speed may be defined in several ways). Various timed continuous PN models have been defined and they correspond to a specific calculation of the firing speeds. They provide good approximations for performance evaluation when a PN contains a large number of tokens. Modeling a number of parts in a buffer by a real number may generally be an acceptable approximation. However, the s...

Petri nets for modeling of dynamic systems—a survey

Abstract Petri nets enable a discrete event system of any kind whatsoever to be modeled. They present two interesting characteristics. Firstly they make it possible to model and visualize behaviors comprising concurrency, synchronization and resource sharing. Secondly the theoretical results concerning them are plentiful. The aim of this paper is to present the basic concept relative to Petri nets and the various classes of derived models which can be used for dynamic system modeling. The tool enables qualitative and quantitative analysis and its numerous applications have been still further increased by a number of research workers to enable more condensed descriptions, even where the time factor intervenes, such as synchronized, timed, stochastic, colored and continuous models. Each of these models thus has its own specific character and privileged fields of application. Nevertheless, the ordinary Petri net forms a common basis: it may be likened to a ‘common language’ allowing dialogue between persons of very varied training backgrounds.

Autonomous And Timed Continous Petri Nets

Since an autonomous continuous Petri net is presented as a limit case of autonomous discrete Petri nets, this new model thus preserves most of the properties of classical Petri nets.

A modelling and analysis tool for discrete events systems: continuous Petri net

Autonomous and timed continuous Petri nets are defined. The autonomous model is presented as a limit case of autonomous discrete Petri nets and thus preserves most of the properties of classical Petri nets. A timed continuous Petri net, with constant firing speeds associated with transitions, is obtained from a timed discrete Petri net. This model has interesting properties such as marking and firing invariants, but its main interest is the construction of the evolution graph. This graph represents the behaviour of the system and contains a finite number of nodes, which allows very short simulations duration in comparison with discrete model simulations. The approximation given by the continuous model is often satisfactory, especially in the case of large markings.

Reduction of constraints for controller synthesis based on safe Petri Nets

In this paper, we present an efficient method based on safe Petri Nets to construct a controller. A set of linear constraints allows forbidding the reachability of specific states. The number of these so-called forbidden states, and consequently the number of constraints, are large and lead to a large number of control places. A systematic method to reduce the size and the number of constraints for safe Petri Nets is offered. By using a method based on Petri Net invariants, maximal permissive controllers are determined.

Combining hybrid Petri nets and hybrid automata

Hybrid systems have received much attention and a number of different models have been proposed in order to establish a mathematical framework which is able to handle both continuous and discrete aspects. Our research is focused on two models: hybrid automata and hybrid Petri nets (hybrid PNs). First, we deal with studying the hybrid PN functioning. An algorithm is proposed for constructing the hybrid automaton associated with a given hybrid PN. Next, we present the quantitative analysis of hybrid systems modeled by hybrid PN. The approach uses the reachability analysis of hybrid automaton to characterize the periodic functioning of a hybrid PN.

The supervised control of discrete event dynamic systems: a new approach

The objective of the supervisory control theory of discrete event dynamic systems (DEDS), first introduced by Ramadge and Wonham (1989), is to design supervisors in such a way that a process coupled with the supervisors behaves according to logical constraints. In this framework, a supervisor can prevent some events from occurring but cannot force any event to appear. Nevertheless, most processes require the addition of an external control agent that forces some events to occur. This has led us to define the supervised control concept. In this new approach, control and supervision are clearly separated. This provides a hierarchical frame that permits us to formalize and systematize the transition from the synthesis to the implementation of the control. Grafcet is a powerful description tool that offers a great conciseness for modelling. In this paper, this tool is intensively used for the supervised control design.

Asymptotic continuous Petri nets: an efficient approximation of discrete event systems

Two continuous Petri net (CPN) models involving time are defined. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The first model considers constant firing speeds (constant-speed CPN, CCPN). It is very easy to simulate. The second model considers firing speeds depending on the marking (variable speed CPN, VCPN). It provides a better approximation, but its simulation is longer because the markings and speeds are given by differential equations. The authors introduce a third model, which has the advantages of the two preceding ones. This model represents the asymptotic behavior of the VCPN. Their precision is similar. It is as easy to simulate as the CCPN.<<ETX>>

Modeling and simulation of water distribution systems using timed hybrid Petri nets

This paper deals with modeling and simulation of water distribution systems using Hybrid Petri Nets. A methodology for building a Timed Hybrid Petri Net (THPN) model is proposed; the model is derived from a set of equations describing conservation of mass and energy that specify the behaviour of a water distribution network. A simulation technique for the execution of a THPN in which the transitions firing velocities are established from the linearised conservation of energy equations is presented; it shows both transient and steady state for the analysis of hydraulic networks. Based on this technique, a simulator in Matlab has been developed.

Asymptotic continuous Petri nets

A Petri net is basically a discrete model. However, continuous Petri nets, such that the markings are real numbers have been defined. Two continuous Petri net models involving time have been drawn up. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The former considers constant firing speeds (CCPN) and is very easy to simulate (few events have to be considered, even when it approximates a timed Petri net with many reachable markings). The latter considers firing speeds depending on the marking (VCPN). Although it provides a better approximation, its simulation is longer because the markings and speeds are given by differential equations. This paper introduces a third model (ACPN) which presents the advantages of the two preceding ones. In most cases, this model represents the asymptotic behavior of the VCPN. Then their precisions are similar. Since the firing speeds of the ACPN are constant, it is as easy to simulate as the CCPN.