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

Structural Sequence Detectability in Free Choice Interpreted Petri Nets

This paper is concerned with the structural sequence detectability problem in Free Choice Interpreted Petri nets, i.e. with the possibility of recovering the firing transition sequence in Free Choice Interpreted Petri nets using the output information when the initial marking is unknown. Based on the Free Choice Interpreted Petri net structure, three relationships are proposed which are devoted to capture the confusion over the transitions. These relationships depend on interpreted Petri nets structures such as T-invariants, P-Invariants, attribution and distribution places. Thus, the approach herein presented exploits the interpreted Petri nets structural information in order to determine the structural sequence detectability of an interpreted Petri net.Consejo Nacional de Ciencia y Tecnologí

Sistema en lazo cerrado para el diagnóstico de fallos de sistemas de eventos discretos utilizando redes de Petri interpretadas

Este trabajo presenta la implementación de un diagnosticador de fallos en línea, para la detección de fallos operacionales presentes en la planta piloto de procesamiento de aguas, en el marco del proyecto REAGRITECH de la cátedra Unesco de sostenibilidad, modelada como un sistema de eventos discretos (SED), haciendo uso de redes de Petri interpretadas (IPN). Se realiza un análisis de funcionamiento del sistema real, del cual se identifican algunas escenas de funcionamiento, que permiten la construcción de un controlador encargado de representar, de forma simulada, el comportamiento real de la planta. A partir de este, se obtiene una matriz de información de entradas-salidas (E/S), donde las entradas corresponden a las señales de mando de control, y las salidas son las señales de sensores. Estos datos se ingresan como parámetros a un algoritmo de identificación, que entrega como resultado el modelo de la IPN identificado a partir de los datos, es decir, información de una IPN: matriz de incidencia A, función de entrada (Fe) con las etiquetas asociadas a las transiciones, la función de salida (Fs) y una matriz de salida φ que relaciona los sensores con cada plaza del sistema. Con base en el modelo identificado se realiza un análisis de detectabilidad para saber si el sistema es detectable o no por eventos, y se construye un diagnosticador a partir de fallos predefinidos. Se concluye que el diagnosticador implementado es capaz de detectar fallos presentes en la planta piloto de procesamiento de agua, en el marco del proyecto REAGRITECH, haciendo un análisis del marcado en los lugares de diagnóstico y en los lugares Post de riesgos del sistema

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. IEEE Transactions on Automation Science and Engineering, 8(4), 794-804. doi:10.1109/tase.2011.2156783Hiraishi, K. (1992). Construction of a class of safe Petri nets by presenting firing sequences. Lecture Notes in Computer Science, 244-262. doi:10.1007/3-540-55676-1_14Estrada-Vargas, A. P., López-Mellado, E., & Lesage, J.-J. (2010). A Comparative Analysis of Recent Identification Approaches for Discrete-Event Systems. Mathematical Problems in Engineering, 2010, 1-21. doi:10.1155/2010/453254Shaolong Shu, & Feng Lin. (2013). I-Detectability of Discrete-Event Systems. IEEE Transactions on Automation Science and Engineering, 10(1), 187-196. doi:10.1109/tase.2012.2215959Li, L., & Hadjicostis, C. N. (2011). Least-Cost Transition Firing Sequence Estimation in Labeled Petri Nets With Unobservable Transitions. IEEE Transactions on Automation Science and Engineering, 8(2), 394-403. doi:10.1109/tase.2010.2070065Supavatanakul, P., Lunze, J., Puig, V., & Quevedo, J. (2006). 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. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 42(2), 416-429. doi:10.1109/tsmca.2011.2169950Ramirez-Trevino, A., Ruiz-Beltran, E., Rivera-Rangel, I., & Lopez-Mellado, E. (2007). Online Fault Diagnosis of Discrete Event Systems. A Petri Net-Based Approach. IEEE Transactions on Automation Science and Engineering, 4(1), 31-39. doi:10.1109/tase.2006.872120Toutenburg, H. (1974). Fleiss, J. L.: Statistical Methods for Rates and Proportions. John Wiley & Sons, New York-London-Sydney-Toronto 1973. XIII, 233 S. Biometrische Zeitschrift, 16(8), 539-539. doi:10.1002/bimj.19740160814Livingston, E. H., & Cassidy, L. (2005). Statistical Power and Estimation of the Number of Required Subjects for a Study Based on the t-Test: A Surgeon’s Primer. Journal of Surgical Research, 126(2), 149-159. doi:10.1016/j.jss.2004.12.013Ruppert, D. (2011). Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. doi:10.1007/978-1-4419-7787-

DETECCIÓN ACTIVA DE FALTAS EN SISTEMAS DE EVENTOS DISCRETOS

ResumenEl objetivo de este trabajo es presentar una propuesta de solución de Diagnóstico Activo en Sistemas de Eventos Discretos modelado por redes de Petri. La propuesta se basa en un controlador llamado Circuito de Regulación Inteligente que reduce la distancia relativa entre las transiciones que modelan faltas y las del resto de la red de Petri, permitiendo la detección y diagnóstico de faltas mientras se mantiene la vivacidad del sistema y se reduce la flexibilidad del sistema sólo en los estados requeridos. Finalmente, los resultados presentados se ilustran en un ejemplo.Palabras Claves: Detección activa, diagnosticabilidad, redes de Petri, sistemas de eventos discretos. ACTIVE FAULT DETECTION IN DISCRETE EVENT SYSTEMSAbstractThe aim of this work is to present a proposal of Active Diagnosis in Discrete Event Systems modeled by Petri nets. This approach is based on a controller named Intelligent Regulation Circuit which reduces the relative distance among the system transition allow in the detection and diagnosis of faults while maintaining the liveness of the system. Finally, the results presented are illustrated by an example.Keywords: Active detection, diagnosability, discrete event system, Petri nets

Modelling and Adaptive Control; Proceedings of an IIASA Conference, Sopron, Hungary, July 1986

One of the main purposes of the workshop on Modelling and Adaptive Control at Sopron, Hungary, was to give an overview of both traditional and recent approaches to the twin theories of modelling and control which ultimately must incorporate some degree of uncertainty. The broad spectrum of processes for which solutions of some of these problems were proposed was itself a testament to the vitality of research on these fundamental issues. In particular, these proceedings contain new methods for the modelling and control of discrete event systems, linear systems, nonlinear dynamics and stochastic processes

Advances in Robotics, Automation and Control

The book presents an excellent overview of the recent developments in the different areas of Robotics, Automation and Control. Through its 24 chapters, this book presents topics related to control and robot design; it also introduces new mathematical tools and techniques devoted to improve the system modeling and control. An important point is the use of rational agents and heuristic techniques to cope with the computational complexity required for controlling complex systems. Through this book, we also find navigation and vision algorithms, automatic handwritten comprehension and speech recognition systems that will be included in the next generation of productive systems developed by man

SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION

Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency. In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications

A Compass to Controlled Graph Rewriting

With the growing complexity and autonomy of software-intensive systems, abstract modeling to study and formally analyze those systems is gaining on importance. Graph rewriting is an established, theoretically founded formalism for the graphical modeling of structure and behavior of complex systems. A graph-rewriting system consists of declarative rules, providing templates for potential changes in the modeled graph structures over time. Nowadays complex software systems, often involving distributedness and, thus, concurrency and reactive behavior, pose a challenge to the hidden assumption of global knowledge behind graph-based modeling; in particular, describing their dynamics by rewriting rules often involves a need for additional control to reflect algorithmic system aspects. To that end, controlled graph rewriting has been proposed, where an external control language guides the sequence in which rules are applied. However, approaches elaborating on this idea so far either have a practical, implementational focus without elaborating on formal foundations, or a pure input-output semantics without further considering concurrent and reactive notions. In the present thesis, we propose a comprehensive theory for an operational semantics of controlled graph rewriting, based on well-established notions from the theory of process calculi. In the first part, we illustrate the aforementioned fundamental phenomena by means of a simplified model of wireless sensor networks (WSN). After recapitulating the necessary background on DPO graph rewriting, the formal framework used throughout the thesis, we present an extensive survey on the state of the art in controlled graph rewriting, along the challenges which we address in the second part where we elaborate our theoretical contributions. As a novel approach, we propose a process calculus for controlled graph rewriting, called RePro, where DPO rule applications are controlled by process terms closely resembling the process calculus CCS. In particular, we address the aforementioned challenges: (i) we propose a formally founded control language for graph rewriting with an operational semantics, (ii) explicitly addressing concurrency and reactive behavior in system modeling, (iii) allowing for a proper handling of process equivalence and action independence using process-algebraic notions. Finally, we present a novel abstract verification approach for graph rewriting based on abstract interpretation of reactive systems. To that end, we propose the so-called compasses as an abstract representation of infinite graph languages and demonstrate their use for the verification of process properties over infinite input sets