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

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. The identified model is a deterministic generator of the observed language.The identification method also includes an algorithm that determines when the identification process is over.This work was supported by a Grant from the Universidad del Cauca, reference 2.3-31.2/05 2011.Muñoz-Añasco, DM.; Correcher Salvador, A.; García Moreno, E.; Morant Anglada, FJ. (2014). Identification of Stochastic Timed Discrete Event Systems with st-IPN. Mathematical Problems in Engineering. 2014:1-21. https://doi.org/10.1155/2014/835312S1212014Cassandras, C. G., & Lafortune, S. (Eds.). (2008). Introduction to Discrete Event Systems. doi:10.1007/978-0-387-68612-7Yingwei Zhang, Jiayu An, & Chi Ma. (2013). Fault Detection of Non-Gaussian Processes Based on Model Migration. IEEE Transactions on Control Systems Technology, 21(5), 1517-1526. doi:10.1109/tcst.2012.2217966Ichikawa, A., & Hiraishi, K. (s. f.). Analysis and control of discrete event systems represented by petri nets. Lecture Notes in Control and Information Sciences, 115-134. doi:10.1007/bfb0042308Fanti, M. P., Mangini, A. M., & Ukovich, W. (2013). Fault Detection by Labeled Petri Nets in Centralized and Distributed Approaches. IEEE Transactions on Automation Science and Engineering, 10(2), 392-404. doi:10.1109/tase.2012.2203596Cabasino, M. P., Giua, A., & Seatzu, C. (2010). Fault detection for discrete event systems using Petri nets with unobservable transitions. Automatica, 46(9), 1531-1539. doi:10.1016/j.automatica.2010.06.013Hu, H., Zhou, M., Li, Z., & Tang, Y. (2013). An Optimization Approach to Improved Petri Net Controller Design for Automated Manufacturing Systems. IEEE Transactions on Automation Science and Engineering, 10(3), 772-782. doi:10.1109/tase.2012.2201714Hu, H., Zhou, M., & Li, Z. (2011). Supervisor Optimization for Deadlock Resolution in Automated Manufacturing Systems With Petri Nets. 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Diagnosis of timed automata: Theory and application to the DAMADICS actuator benchmark problem. Control Engineering Practice, 14(6), 609-619. doi:10.1016/j.conengprac.2005.03.028Dotoli, M., Fanti, M. P., & Mangini, A. M. (2008). Real time identification of discrete event systems using Petri nets. Automatica, 44(5), 1209-1219. doi:10.1016/j.automatica.2007.10.014Chen, Y., Li, Z., Khalgui, M., & Mosbahi, O. (2011). Design of a Maximally Permissive Liveness- Enforcing Petri Net Supervisor for Flexible Manufacturing Systems. IEEE Transactions on Automation Science and Engineering, 8(2), 374-393. doi:10.1109/tase.2010.2060332Murata, T. (1989). Petri nets: Properties, analysis and applications. Proceedings of the IEEE, 77(4), 541-580. doi:10.1109/5.24143Ramirez-Trevino, A., Ruiz-Beltran, E., Aramburo-Lizarraga, J., & Lopez-Mellado, E. (2012). Structural Diagnosability of DES and Design of Reduced Petri Net Diagnosers. 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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

Diagnosis on a sliding window for partially observable Petri nets

summary:In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length $h$. Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. The proposed approach consists in exploiting a subset of $h$ observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a "forgetfulness" of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As the analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these irrelevant basis markings based on linear programming is proposed

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

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

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