Minimum-time control for structurally persistent continuous Petri nets and the application in distributed Control

In this report, we first address the minimum-time control problem of structurally persistent timed continuous Petri Net systems (ContPN). In particular, an ON-OFF controller is proposed to drive the system from a given initial marking to the final marking in minimum-time. The controller is developed first for the discrete-time system ensuring that all transitions are fired as fast as possible in each sampling period until the required total firing counts are reached. After that, they are stopped suddenly. By taking the limit of the sampling period, the controller for continuous-time systems is obtained. Simplicity and the fact that it ensures minimum-time are the main advantages of the controller. A manufacturing system is taken as case study to illustrate the control strategy. In a distributed controlled system, normally a complex dynamic system, the controllers are not centralized in one location, but are distributed in subsystems. We try to apply the ON-OFF controller into the distributed control of large scale systems modeled with timed continuous Petri net. The original net system is first structurally decompose into smaller subnets through sets of places. Then the ON-OFF controller is applied in controlling each subsystem. Algorithms are proposed to compute admissible control laws for the local subsystems in a distributed way. It is proved that with that control laws, the final state can be reached in minimum time

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

http://dx.doi.org/10.1093/bib/bbn026Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach { Qualitative Petri nets, and quantitative approaches { Continuous Petri Nets and Ordinary Differential Equations. We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present ..

Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

A case study in model-driven synthetic biology

We report on a case study in synthetic biology, demonstrating the modeldriven design of a self-powering electrochemical biosensor. An essential result of the design process is a general template of a biosensor, which can be instantiated to be adapted to specific pollutants. This template represents a gene expression network extended by metabolic activity. We illustrate the model-based analysis of this template using qualitative, stochastic and continuous Petri nets and related analysis techniques, contributing to a reliable and robust design

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Pemodelan Sistem Ketenagalistrikan Skala Kecil Terisolasi menggunakan Jaring Petri Kontinu Berwaktu

Utilization of isolated small-scale electricity system for supporting power supplies will continue to rise. This system is used for various purposes, particularly to supply the electricity needs of remote areas. To obtain a good performance of the system, the system requires regulatory mechanisms that coordinate system components. This mechanism is often called as energy management system. To develop an energy management system, generally the researchers used a mathematical model of the electricity system. The complexity and performance of the energy management system is very dependent on the mathematical model. In this study, a mathematical model of the electricity system will be deployed using Petri Net Model as a kind of discrete-event model. Some types of Petri nets have been used in designing an energy management system, however the implementation of Timed Continuous Petri Net (TCPN) developed by J.Julvez et al. not yet published. In this study, TCPN model for isolated small-scale electricity system developed is simulated using software called SimHPN. Our simulation results show that the developed model is valid. Although the new model is applied to a simple system, this model can be developed for more complex systemsKeywords : Isolated Small-Scale Electricity System, Timed Continuous Petri Net, Energy Management SystemAbstrak— Pemanfaatan sistem ketenagalistrikan skala kecil terisolasi untuk mendukung pasokan listrik akan terus meningkat. Sistem ini digunakan dengan berbagai tujuan khususnya untuk memasok kebutuhan listrik daerah terpencil. Untuk mendapatkan kinerja sistem yang bagus, sistem ini membutuhkan mekanisme pengaturan yang mengkoordinasikan komponen-komponen sistem. Mekanisme ini sering diistilahkan dengan sistem manajemen energi. Untuk mengembangkan sistem manajemen energi, umumnya  para peneliti menggunakan model matematik sistem ketenagalistrikan. Kompleksitas dan kinerja sistem manajemen energi sangat bergantung pada model matematika tersebut. Dalam penelitian ini, model matematik sistem ketenagalistrikan akan diturunkan dengan menggunakan model jaring petri sebagai salah satu jenis model kejadian diskrit. Beberapa jenis jaring petri sudah digunakan dalam merancang sistem manajemen energi, tetapi penerapan jaring petri jenis kontinu berwaktu (Timed Continuous Petri Net/TCPN) yang dikembangkan oleh J.Julvez dkk. belum dipublikasikan. Dalam penelitian ini, model TCPN sistem ketenagalistrikan terisolasi yang dikembangkan disimulasikan dengan menggunakan perangkat lunak SimHPN.  Hasil simulasi memperlihatkan bahwa model yang dikembangkan valid. Meskipun model baru diterapkan pada sistem yang sederhana, model ini dapat dikembangkan untuk sistem yang lebih kompleks.Kata Kunci : Sistem Ketenagalistrikan Kecil Terisolasi,  Model Jaring Petri Kontinu Berwaktu, Sistem Majemen Energ

Redes de Petri híbridas adaptativas : alcanzabilidad y ausencia de bloqueos

Las redes de Petri (RdP) son un paradigma formal ampliamente aceptado para el modelado de sistemas de eventos discretos. No obstante, con poblaciones de gran tamaño, aparece el problema de la explosión de estados (crecimiento exponencial del tamaño del conjunto de estados alcanzables). Una manera de paliar este problema consiste en fluidificar el formalismo y considerar redes de Petri continuas, que permiten abordar de manera eficiente el estudio de los sistemas mediante técnicas lineales de análisis. Sin embargo, las RdP continuas no siempre preservan sus propiedades, como por ejemplo la ausencia de bloqueos. En este Trabajo se introduce, formaliza y estudia un formalismo nuevo, denominado redes de Petri híbridas adaptativas (HAPN), que combina comportamiento continuo y discreto: El comportamiento de las transiciones de la red adaptativa es variable: una transición se comporta como continua si su carga de trabajo supera un umbral establecido inicialmente, en caso contrario se comporta como discreta. Estas redes pueden aproximar mejor las redes discretas, mientras que cuando las poblaciones son elevadas el comportamiento es continuo y las técnicas lineales son aplicables, evitando el problema de la explosión de estados. De esta manera, las HAPN constituyen un marco conceptual muy general que incluye a las redes de Petri discretas,continuas e híbridas. En este trabajo, se ha definido formalmente el formalismo de redes de Petri adaptativas. A continuación, se ha caracterizado el conjunto de marcados alcanzables de las redes de Petri adaptativas, así como se compara con el de las RdP discretas. Por ultimo, se ha estudiado la propiedad de ausencia de bloqueos: se trata de determinar si la red adaptativa preserva la ausencia de bloqueos de la red discreta con misma estructura y marcado inicial