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

Diagnosability Analysis of Labeled Time Petri Net Systems

In this paper, we focus on two notions of diagnosability for labeled Time Petri net (PN) systems: K-diagnosability implies that any fault occurrence can be detected after at most K observations, while τ-diagnosability implies that any fault occurrence can be detected after at most τ time units. A procedure to analyze such properties isprovided.The proposedapproach uses the Modified State Class Graph, a graph the authors recently introduced for the marking estimation of labeled Time PN systems,which providesan exhaustive description of the system behavior. A preliminary diagnosabilty analysis of the underlying logic system based on classical approaches taken from the literature is required. Then, the solution of some linear programming problems should be performed to take into account the timing constraints associated with transitions

Minimum Initial Marking Estimation in Labeled Petri Nets With Unobservable Transitions

In the literature, researchers have been studying the minimum initial marking (MIM) estimation problem in the labeled Petri nets with observable transitions. This paper extends the results to labeled Petri nets with unobservable transitions (with certain special structure) and proposes algorithms for the MIM estimation (MIM-UT). In particular, we assume that the Petri net structure is given and the unobservable transitions in the net are contact-free. Based on the observation of a sequence of labels, our objective is to find the set of MIM(s) that is(are) able to produce this sequence and has(have) the smallest total number of tokens. An algorithm is developed to find the set of MIM(s) with polynomial complexity in the length of the observed label sequence. Two heuristic algorithms are also proposed to reduce the computational complexity. An illustrative example is also provided to demonstrate the proposed algorithms and compare their performance

VERIFICATION AND APPLICATION OF DETECTABILITY BASED ON PETRI NETS

In many real-world systems, due to limitations of sensors or constraints of the environment, the system dynamics is usually not perfectly known. However, the state information of the system is usually crucial for the purpose of decision making. The state of the system needs to be determined in many applications. Due to its importance, the state estimation problem has received considerable attention in the discrete event system (DES) community. Recently, the state estimation problem has been studied systematically in the framework of detectability. The detectability properties characterize the possibility to determine the current and the subsequent states of a system after the observation of a finite number of events generated by the system. To model and analyze practical systems, powerful DES models are needed to describe the different observation behaviors of the system. Secondly, due to the state explosion problem, analysis methods that rely on exhaustively enumerating all possible states are not applicable for practical systems. It is necessary to develop more efficient and achievable verification methods for detectability. Furthermore, in this thesis, efficient detectability verification methods using Petri nets are investigated, then detectability is extended to a more general definition (C-detectability) that only requires that a given set of crucial states can be distinguished from other states. Formal definitions and efficient verification methods for C-detectability properties are proposed. Finally, C-detectability is applied to the railway signal system to verify the feasibility of this property: 1. Four types of detectability are extended from finite automata to labeled Petri nets. In particular, strong detectability, weak detectability, periodically strong detectability, and periodically weak detectability are formally defined in labeled Petri nets. 2. Based on the notion of basis reachability graph (BRG), a practically efficient approach (the BRG-observer method) to verify the four detectability properties in bounded labeled Petri nets is proposed. Using basis markings, there is no need to enumerate all the markings that are consistent with an observation. It has been shown by other researchers that the size of the BRG is usually much smaller than the size of the reachability graph (RG). Thus, the method improves the analysis efficiency and avoids the state space explosion problem. 3. Three novel approaches for the verification of the strong detectability and periodically strong detectability are proposed, which use three different structures whose construction has a polynomial complexity. Moreover, rather than computing all cycles of the structure at hand, which is NP-hard, it is shown that strong detectability can be verified looking at the strongly connected components whose computation also has a polynomial complexity. As a result, they have lower computational complexity than other methods in the literature. 4. Detectability could be too restrictive in real applications. Thus, detectability is extended to C-detectability that only requires that a given set of crucial states can be distinguished from other states. Four types of C-detectability are defined in the framework of labeled Petri nets. Moreover, efficient approaches are proposed to verify such properties in the case of bounded labeled Petri net systems based on the BRG. 5. Finally, a general modeling framework of railway systems is presented for the states estimation using labeled Petri nets. Then, C-detectability is applied to railway signal systems to verify its feasibility in the real-world system. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, the RBC handover procedure is modeled using labeled Petri nets. Then based on the proposed approaches, it is shown that that the RBC handover procedure satisfies strongly C-detectability

State Estimation of Timed Discrete Event Systems and Its Applications

Many industrial control systems can be described as discrete event systems (DES), whose state space is a discrete set where event occurrences cause transitions from one state to another. Timing introduces an additional dimension to DES modeling and control. This dissertation provides two models of timed DES endowed with a single clock, namely timed finite automata (TFA) and generalized timed finite automata (GTFA). In addition, a timing function is defined to associate each transition with a time interval specifying at which clock values it may occur. While the clock of a TFA is reset to zero after each event occurs and the time semantics constrain the dwell time at each discrete state, there is an additional clock resetting function associated with a GTFA to denote whether the clock is reset to a value in a given closed time interval. We assume that the logical and time structure of a partially observable TFA/GTFA is known. The main results are summarized as follows. 1. The notion of a zone automaton is introduced as a finite automaton providing a purely discrete event description of the behaviour of a TFA/GTFA of interest. Each state of a zone automaton contains a discrete state of the timed DES and a zone that is a time interval denoting a range of possible clock values. We investigate the dynamics of a zone automaton and show that one can reduce the problem of investigating the reachability of a given timed DES to the reachability analysis of a zone automaton. 2. We present a formal approach that allows one to construct offline an observer for TFA/GTFA, i.e., a finite structure that describes the state estimation for all possible evolutions. During the online phase to estimate the current discrete state according to each measurement of an observable event, one can determine which is the state of the observer reached by the current observation and check to which interval (among a finite number of time intervals) the time elapsed since the last observed event occurrence belongs. We prove that the discrete states consistent with a timed observation and the range of clock values associated with each estimated discrete state can be inferred following a certain number of runs in the zone automaton. In particular, the state estimation of timed DES under multiple clocks can be investigated in the framework of GTFA. We model such a system as a GTFA with multiple clocks, which generalizes the timing function and the clock resetting function to multiple clocks. 3. As an application of the state estimation approach for TFA, we assume that a given TFA may be affected by a set of faults described using timed transitions and aim at diagnosing a fault behaviour based on a timed observation. The problem of fault diagnosis is solved by constructing a zone automaton of the TFA with faults and a fault recognizer as the parallel composition of the zone automaton and a fault monitor that recognizes the occurrence of faults. We conclude that the occurrence of faults can be analyzed by exploring runs in the fault recognizer that are consistent with a given timed observation. 4. We also study the problem of attack detection in the context of DESs, assuming that a system may be subject to multiple types of attacks, each described by its own attack dictionary. Furthermore, we distinguish between constant attacks, which corrupt observations using only one of the attack dictionaries, and switching attacks, which may use different attack dictionaries at different steps. The problem we address is detecting whether a system has been attacked and, if so, which attack dictionaries have been used. To solve it in the framework of untimed DES, we construct a new structure that describes the observations generated by a system under attack. We show that the attack detection problem can be transformed into a classical state estimation/diagnosis problem for these new structures

Identification of Stochastic Timed Discrete Event Systems with st-IPN

[EN] This paper presents amethod for the identification of stochastic timed discrete event systems, based on the analysis of the behavior of the input and output signals, arranged in a timeline. To achieve this goal stochastic timed interpreted Petri nets are defined.These nets link timed discrete event systems modelling with stochastic time modelling. The procedure starts with the observation of the input/output signals; these signals are converted into events, so that the sequence of events is the observed language. This language arrives to an identifier that builds a stochastic timed interpreted Petri net which generates the same language. 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PetriBaR: A MATLAB Toolbox for Petri Nets Implementing Basis Reachability Approaches

This paper presents a MATLAB toolbox, called PetriBaR, for the analysis and control of Petri nets. PetriBaR is a package of functions devoted to basic Petri net analysis (including the computation of T-invariants, siphons, reachability graph, etc.), monitor design, reachability analysis, state estimation, fault diagnosis, and opacity verification. In particular, the functions for reachability analysis, state estimation, fault diagnosis, and opacity verification exploit the construction of the Basis Reachability Graph to avoid the exhaustive enumeration of the reachable set, thus leading to significant advantages in terms of computational complexity. All functions of PetriBaR are introduced in detail clarifying the syntax to be used to run them. Finally, they are illustrated via a series of numerical examples. PetriBaR is available online for public access