Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1

Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested

Petri Nets at Modelling and Control of Discrete-Event Systems with Nondeterminism - Part 2

Discrete-Event Systems (DES) are discrete in nature. Petri Nets (PN) are one of the most widespread tools for DES modelling, analyzing and control. Different kinds of PN can be used for such purposes. Some of them were described in [3], being the first part of this paper. Here, the applicability of Labelled PN (LbPN) and Interpreted PN (IPN) for modelling and control of nondeterministic DES, especially with uncontrollable and/or unobservable transitions in the models, will be pointed out. Moreover, another kinds of nondeterminism in DES (errors, failures) will be modelled, and the possibilities of the error recovery of failed system will be presented

Automatic Control Synthesis for Agents and Their Cooperation in MAS

Automatic synthesis of control for a kind of DES (discrete-event systems) is discussed and an approach to it is proposed and presented. The approach consists in the proposal of the control synthesis procedure based on bipartite directed graphs yielding both the feasible control trajectories and the corresponding state ones. Soundness of the approach is tested on examples. Then, the usage of the approach is combined with the supervisor synthesis in order to complement it. Applicability of such approach is demonstrated by means of several illustrative examples of both the single agents and the agent cooperation in MAS

Modelling, Analysing and Control of Interactions Among Agents in MAS

An alternative approach to modelling and analysis of interactions among agents in multiagent systems (MAS) and to their control is presented in analytical terms. The attention is focused especially on the negotiation process. However, the possibility of another form of the communication is mentioned too. The reachability graph of the Petri net (PN)-based model of MAS is found as well as the space of feasible states. Trajectories representing the interaction processes among agents in MAS are computed by means of the mutual intersection of both the straight-lined reachability tree (from a given initial state towards the terminal one) and the backtracking reachability tree (from the desired terminal state towards the initial one, however oriented towards the terminal state). Control interferences are obtained on the basis of the most suitable trajectory chosen from the set of feasible ones

Modelling and Control of Resource Allocation Systems within Discrete Event Systems by Means of Petri Nets – Part 1: Invariants, Siphons and Traps in Deadlock Avoidance

Solving the deadlocks avoidance problem in Resource Allocation Systems (RAS) in Discrete-Event Systems (DES) is a rife problem, especially in Flexible Manufacturing Systems (FMS), alias Automated Manufacturing Systems (AMS). Petri Nets (PN) are an effectual tool often used at this procedure. In principle, there are two basic approaches how to deal with deadlocks in RAS based on PN. They are listed and illustrated here. First of the approaches is realized by means of the supervisor based on P-invariants of PN, while the second one is realized by means of the supervisor based on PN siphons. While the first approach needs to know the reachability graph/tree (RG/RT) expressing the causality of the development of the PN model of RAS, in order to find (after its thorough analysis) the deadlocks, the second approach needs the thorough analysis of the PN model structure by means of finding siphons and traps. Next, both approaches will be applied on the same PN model of RAS and the effectiveness of the achievement of their results will be compared and evaluated. Several simple illustrative examples will be introduced. For the in-depth analysis of the problem of deadlock avoiding, next Part 2 of this paper is prepared, where the newest research will be introduced and illustrated on more complicated examples. If necessary (because of the limited length of particular papers), also the third part – Part 3, will be prepared

Timed and Hybrid Petri Nets at Solving Problems of Computational Intelligence

Timed Petri nets (TPN) and hybrid Petri nets (HPN), more precisely first-order HPN (FOHPN), are used here in order to model, analyse and control discrete-event systems (DES) and hybrid systems (HS) of different kinds consisting of cooperating subsystems (modules, agents). Foremost, principles of the particular kinds of Petri nets (PN), including the primary place/transition PN (P/T PN), are explained. Then, two methods of the supervision are introduced. Finally, the corresponding kinds of PN are applied in four case studies in order to solve the problems of modelling, analysing and control. Namely, the throughput of transport systems (rail and road), flexible manufacturing systems (FMS) and the workflow (WF) of the evacuation process from an endangered area (EA) are handled

Modelling and control of flexible manufacturing systems by means of interpreted Petri nets

Because flexible manufacturing systems (FMS) are discrete event systems (DES), their modelling and control by means of Petri nets (PN) is widely used. While PN transitions are observable and controllable and PN places are measurable, place/transition PN (P/T PN) are suffcient for this aim. However, when some PN transitions are unobservable and/or uncontrollable and some places are non-measurable/unobservable, P/T PN are insufficient for modelling and especially for control. In such a case interpreted Petri nets (IPN) seem to be an appropriate replacement for P/T PN. In this paper a possibility of usage of IPN for FMS modelling and control is pointed out. Illustrative examples as well as the case study on a robotized assembly cell are introduced. By means of using timed PN (TPN) also the performance evaluation of the IPN model of controlled plant is accomplished whereby the simulation in Matlab

Failures in discrete-event systems and dealing with them by means of Petri nets

Abstract An approach based on Petri nets pointing to the manner how to deal with failures in discrete-event systems is presented. It uses the reachability tree and/or reachability graph of the Petri net-based model of the real system as well as the synthesis of a supervisor to remove the possible deadlock(s). To illustrate the applicability of the approach to the detection and recovery of failures in DES modelled by Petri nets the case study on a railroad crossing is introduced