Strict Minimal Siphon-Based Colored Petri Net Supervisor Synthesis for Automated Manufacturing Systems With Unreliable Resources

Various deadlock control policies for automated manufacturing systems with reliable and shared resources have been developed, based on Petri nets. In practical applications, a resource may be unreliable. Thus, the deadlock control policies proposed in previous studies are not applicable to such applications. This paper proposes a two-step robust deadlock control strategy for systems with unreliable and shared resources. In the first step, a live (deadlock-free) controlled system that does not consider the failure of resources is derived by using strict minimal siphon control. The second step deals with deadlock control issues caused by the failures of the resources. Considering all resource failures, a common recovery subnet based on colored Petri nets is proposed for all resource failures in the Petri net model. The recovery subnet is added to the derived system at the first step to make the system reliable. The proposed method has been tested using an automated manufacturing system deployed at King Saud University.publishedVersio

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

On the decidability of problems in liveness of controlled Discrete Event Systems modeled by Petri Nets

A Discrete Event System (DES) is a discrete-state system, where the state changes at discrete-time instants due to the occurrence of events. Informally, a liveness property stipulates that a 'good thing' happens during the evolution of a system. Some examples of liveness properties include starvation freedom -- where the 'good thing' is the process making progress; termination -- in which the good thing is for an evolution to not run forever; and guaranteed service -- such as in resource allocation systems, when every request for resource is satisfied eventually. In this thesis, we consider supervisory policies for DESs that, when they exist, enforce a liveness property by appropriately disabling a subset of preventable events at certain states in the evolution of DES. One of the main contributions of this thesis is the development of a system-theoretic framework for the analysis of Liveness Enforcing Supervisory Policies (LESPs) for DESs. We model uncertainties in the forward- and feedback-path, and present necessary and sufficient conditions for the existence of Liveness Enforcing Supervisory Policies (LESPs) for a general model of DESs in this framework. The existence of an LESP reduces to the membership of the initial state to an appropriately defined set. The membership problem is undecidable. For characterizing decidable instances of this membership problem, we consider a modeling paradigm of DESs known as Petri Nets, which have applications in modeling concurrent systems, software design, manufacturing systems, etc. Petri Net (PN) models are inherently monotonic in the sense that if a transition (which loosely represents an event of the DES) can fire from a marking (a non-negative integer-valued vector that represents the state of the DES being modeled), then it can also fire from any larger marking. The monotonicity creates a possibility of representing an infinite-state system using what can be called a "finite basis" that can lead to decidability. However, we prove that several problems of our interest are still undecidable for arbitrary PN models. That is, informally, a general PN model is still too powerful for the analysis that we are interested in. Much of the thesis is devoted to the characterization of decidable instances of the existence of LESPs for arbitrary PN models within the system-theoretic framework introduced in the thesis. The philosophical implication of the results in this thesis is the existence of what can be called a "finite basis" of an infinite state system under supervision, on which the membership tests can be performed in finite time; hence resulting in the decidability of problems and finite-time termination of algorithms. The thesis discusses various scenarios where such a finite basis exists and how to find them

Maximal good step graph methods for reducing the generation of the state space

This paper proposes an effective method based on the two main partial order techniques which are persistent sets and covering step graph techniques, to deal with the state explosion problem. First, we introduce a new definition of sound steps, the firing of which enables to extremely reduce the state space. Then, we propose a weaker sufficient condition about how to find the set of sound steps at each current marking. Next, we illustrate the relation between maximal sound steps and persistent sets, and propose a concept of good steps. Based on the maximal sound steps and good steps, a construction algorithm for generating a maximal good step graph (MGSG) of a Petri net (PN) is established. This algorithm first computes the maximal good step at each marking if there exists one, otherwise maximal sound steps are fired at the marking. Furthermore, we have proven that an MGSG can effectively preserve deadlocks of a Petri net. Finally, the change performance evaluation is made to demonstrate the superiority of our proposed method, compared with other related partial order techniques

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

An Evaluation Framework for Comparative Analysis of Generalized Stochastic Petri Net Simulation Techniques

Availability of a common, shared benchmark to provide repeatable, quantifiable, and comparable results is an added value for any scientific community. International consortia provide benchmarks in a wide range of domains, being normally used by industry, vendors, and researchers for evaluating their software products. In this regard, a benchmark of untimed Petri net models was developed to be used in a yearly software competition driven by the Petri net community. However, to the best of our knowledge there is not a similar benchmark to evaluate solution techniques for Petri nets with timing extensions. In this paper, we propose an evaluation framework for the comparative analysis of generalized stochastic Petri nets (GSPNs) simulation techniques. Although we focus on simulation techniques, our framework provides a baseline for a comparative analysis of different GSPN solvers (e.g., simulators, numerical solvers, or other techniques). The evaluation framework encompasses a set of 50 GSPN models including test cases and case studies from the literature, and a set of evaluation guidelines for the comparative analysis. In order to show the applicability of the proposed framework, we carry out a comparative analysis of steady-state simulators implemented in three academic software tools, namely, GreatSPN, PeabraiN, and TimeNET. The results allow us to validate the trustfulness of these academic software tools, as well as to point out potential problems and algorithmic optimization opportunities

Discrete Event Systems: Models and Applications; Proceedings of an IIASA Conference, Sopron, Hungary, August 3-7, 1987

Work in discrete event systems has just begun. There is a great deal of activity now, and much enthusiasm. There is considerable diversity reflecting differences in the intellectual formation of workers in the field and in the applications that guide their effort. This diversity is manifested in a proliferation of DEM formalisms. Some of the formalisms are essentially different. Some of the "new" formalisms are reinventions of existing formalisms presented in new terms. These "duplications" reveal both the new domains of intended application as well as the difficulty in keeping up with work that is published in journals on computer science, communications, signal processing, automatic control, and mathematical systems theory - to name the main disciplines with active research programs in discrete event systems. The first eight papers deal with models at the logical level, the next four are at the temporal level and the last six are at the stochastic level. Of these eighteen papers, three focus on manufacturing, four on communication networks, one on digital signal processing, the remaining ten papers address methodological issues ranging from simulation to computational complexity of some synthesis problems. The authors have made good efforts to make their contributions self-contained and to provide a representative bibliography. The volume should therefore be both accessible and useful to those who are just getting interested in discrete event systems

Scheduling of flexible manufacturing systems integrating petri nets and artificial intelligence methods.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising

Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties

Towards semantics-driven modelling and simulation of context-aware manufacturing systems

Systems modelling and simulation are two important facets for thoroughly and effectively analysing manufacturing processes. The ever-growing complexity of the latter, the increasing amount of knowledge, and the use of Semantic Web techniques adhering meaning to data have led researchers to explore and combine together methodologies by exploiting their best features with the purpose of supporting manufacturing system's modelling and simulation applications. In the past two decades, the use of ontologies has proven to be highly effective for context modelling and knowledge management. Nevertheless, they are not meant for any kind of model simulations. The latter, instead, can be achieved by using a well-known workflow-oriented mathematical modelling language such as Petri Net (PN), which brings in modelling and analytical features suitable for creating a digital copy of an industrial system (also known as "digital twin"). The theoretical framework presented in this dissertation aims to exploit W3C standards, such as Semantic Web Rule Language (SWRL) and Web Ontology Language (OWL), to transform each piece of knowledge regarding a manufacturing system into Petri Net modelling primitives. In so doing, it supports the semantics-driven instantiation, analysis and simulation of what we call semantically-enriched PN-based manufacturing system digital twins. The approach proposed by this exploratory research is therefore based on the exploitation of the best features introduced by state-of-the-art developments in W3C standards for Linked Data, such as OWL and SWRL, together with a multipurpose graphical and mathematical modelling tool known as Petri Net. The former is used for gathering, classifying and properly storing industrial data and therefore enhances our PN-based digital copy of an industrial system with advanced reasoning features. This makes both the system modelling and analysis phases more effective and, above all, paves the way towards a completely new field, where semantically-enriched PN-based manufacturing system digital twins represent one of the drivers of the digital transformation already in place in all companies facing the industrial revolution. As a result, it has been possible to outline a list of indications that will help future efforts in the application of complex digital twin support oriented solutions, which in turn is based on semantically-enriched manufacturing information systems. Through the application cases, five key topics have been tackled, namely: (i) semantic enrichment of industrial data using the most recent ontological models in order to enhance its value and enable new uses; (ii) context-awareness, or context-adaptiveness, aiming to enable the system to capture and use information about the context of operations; (iii) reusability, which is a core concept through which we want to emphasize the importance of reusing existing assets in some form within the industrial modelling process, such as industrial process knowledge, process data, system modelling primitives, and the like; (iv) the ultimate goal of semantic Interoperability, which can be accomplished by adding data about the metadata, linking each data element to a controlled, shared vocabulary; finally, (v) the impact on modelling and simulation applications, which shows how we could automate the translation process of industrial knowledge into a digital manufacturing system and empower it with quantitative and qualitative analytical technics