Modeling by petri net with place invariants for sequential control systems

Petri nets are used to design deadlock control strategies for flexible manufacturing systems (FMS), which typically involve the addition of monitors and the associated arcs to the FMS. The addition of several monitors and associated arcs to first constructed Petri net model significantly complicates the Petri net controller. This paper develops a two-step method for preventing deadlocks based on a colored Petri net and a structurally minimal approach that significantly reduces the number of monitors. In the first step, a vector covering technique is applied to generate a minimal covered sets of first-met bad markings (FBMs) and legal markings that are respectively smaller than the sets of FBMs and legal markings. At one iteration, place invariants (PIs) corresponding to monitors are constructed by solving an integer linear programming problem (ILPP) to prohibit the maximum number of FBMs, while allowing all legal markings in the minimal covering set. The purpose of the ILPP is to maximize the number of FBMs forbidden by the PIs. Then, based on a colored Petri net, all generated monitors are combined into a global control place. Therefore, a supervisor with minimal structural complexity can be constructed. The obtained net model is controlled after the addition of the designed supervisor. Two instances from the literature are considered to illustrate the proposed approach.

On the fluidization of Petri nets and marking homothecy

Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is verification of safety and liveness properties in this model; despite an extensive research effort, some basic problems remain open, which is exemplified by the complexity status of the reachability problem that is still not fully clarified. The liveness problems are known to be closely related to the reachability problem, and various structural properties of nets that are related to liveness have been studied. Somewhat surprisingly, the decidability status of the problem of determining whether a net is structurally live, i.e. whether there is an initial marking for which it is live, remained open for some time; e.g. Best and Esparza (Inf Process Lett 116(6):423–427, 2016. https://doi.org/10.1016/j.ipl.2016.01.011 ) emphasize this open question. Here we show that the structural liveness problem for Petri nets is ExpSpace-hard and decidable. In particular, given a net N and a semilinear set S, it is decidable whether there is an initial marking of N for which the reachability set is included in S; this is based on results by Leroux (28th annual ACM/IEEE symposium on logic in computer science, LICS 2013, New Orleans, LA, USA, June 25–28, 2013, IEEE Computer Society, pp 23–32, 2013. https://doi.org/10.1109/LICS.2013.7 ).

Mobility induces new challenges for dynamic systems, which need a new conceptional treatment: systems, that deal for example with mobile agents, need extended security concepts to handle the risks, induced by foreign, untrusted agents. In this contribution we use object nets to model mobile systems. Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-withinnets paradigm. Object nets are called elementary if the net system has a two levelled structure. In this work we apply structural analysis methods for object nets – namely place invariants – to a simple case study modelling mobile agents.

The theory of regions is an important method to derive an optimal and liveness-enforcing supervisor for a flexible manufacturing systems based on Petri nets. It first partitions the reachability graph into a live zone (LZ) and a deadlock zone (DZ). Then, activity places are used to construct place invariants (PIs) to prevent the system from entering DZ and permit all markings in LZ. This work studies the reduction of the number of places to be considered in the optimal PI designs. First, the concepts of critical transitions and critical activity places are defined, and an algorithm is provided to compute the sets of critical and uncritical activity places. Then, the proof of that only critical activity places need to be considered in such optimal PI designs is established.

Industrial control systems (ICS) can be subject to highly sophisticated attacks which may lead the process towards critical states. Due to the particular context of ICS, protection mechanisms are not always practical, nor sufficient. On the other hand, developing a process-aware intrusion detection solution with satisfactory alert characterization remains an open problem. This paper focuses on process-aware attacks detection in sequential control systems. We build on results from runtime verification and specification mining to automatically infer and monitor process specifications. Such specifications are represented by sets of temporal safety properties over states and events corresponding to sensors and actuators. The properties are then synthesized as monitors which report violations on execution traces. We develop an efficient specification mining algorithm and use filtering rules to handle the large number of mined properties. Furthermore, we introduce the notion of activity and discuss its relevance to both specification mining and attack detection in the context of sequential control systems. The proposed approach is evaluated in a hardware-in-the-loop setting subject to targeted process-aware attacks. Overall, due to the explicit handling of process variables, the solution provides a better characterization of the alerts and a more meaningful understanding of false positives.

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications

The applications of Petri net modeling to the design and operations of sequential control systems (SCSs) are widely developed. Automatic Petri net generation is also possible. The bottleneck in SCS development is the acquisition of knowledge, as the adaptation and utilization of experience have not been done smoothly. The objective of this work is to simplify the acquisition of knowledge and the transition from the specification of the SCS design to Petri net modeling. A Petri-net-based representation is used to explain the acquisition of knowledge in SCSs by learning and to develop a system for Petri net generation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Invariants in the application-oriented specification of control systems

State Machine Based Deadline Analysis of a Programmable Controller for Real-Time Sequential Control Systems

The paper addresses the fault detection problem for discrete event systems modeled by Petri nets (PN). Assuming that the PN structure and initial marking are known, faults are modeled by unobservable transitions. The paper recalls a previously proposed diagnoser that works online and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behavior is normal or exhibits some possible faults. To reduce the on-line computational effort, we prove some results showing that if the unobservable subnet enjoys suitable properties, the algorithm solution may be obtained with low computational complexity. We characterize the properties that the PN modeling the system fault behavior has to fulfill and suitably modify the proposed diagnoser.

Individuals, populations and fluid approximations: A Petri net based perspective

Discrete event systems are modeled compactly by using Petri nets (T. Murata, 1989). Although Petri nets have powerful mathematical verification ability, in many cases, we have to construct the whole state space for verification. A reachability graph is one of the representations of the state space. Petri nets can describe huge systems compactly, but sometimes it is impossible to generate the reachability graph because of an explosion in required computational time and space. A Petri net is called a reversible net, when it can come back to the initial marking from any reachable marking. The paper considers a verification method for reversibility. An unfolding is obtained by unfolding a Petri net, and it preserves reachability information of an original net and structural analysis on it is much easier than on the original net. The article clarifies relations between unfoldings and reversibility, and provides a verification method for reversibility by using unfoldings.

We study the complexity of the reachability problem for a new subclass of Petri nets called simple-circuit Petri nets, which properly contains several well known subclasses such as conflict-free, BPP, normal Petri nets and more. A new decomposition approach is applied to developing an integer linear programming formulation for characterizing the reachability sets of such Petri nets. Consequently, the reachability problem is shown to be NP-complete. The model checking problem for some temporal logics is also investigated for simple-circuit Petri nets.

We study the complexity of the reachability problem for a new subclass of Petri nets called simple-circuit Petri nets, which properly contains several well known subclasses such as conflict-free, BPP, normal Petri nets and more. A new decomposition approach is applied to developing an integer linear programming formulation for characterizing the reachability sets of such Petri nets. Consequently, the reachability problem is shown to be NP-complete. The model checking problem for some temporal logics is also investigated for simple-circuit Petri nets.