Ninth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools, Aarhus, Denmark, October 20-22, 2008

This booklet contains the proceedings of the Ninth Workshop on Practical Use of Coloured Petri Nets and the CPN Tools, October 20-22, 2008. The workshop is organised by the CPN group at the Department of Computer Science, University of Aarhus, Denmark. The papers are also available in electronic form via the web pages: http://www.daimi.au.dk/CPnets/workshop0

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Thermal-aware real-time scheduling using timed continuous Petri Nets

We present a thermal-aware, hard real-time (HRT) global scheduler for a multiprocessor system designed upon three novel techinques. First, we present a modeling methodology based on Timed Continuous Petri nets (TCPN) that yields a complete state variable model, including job arrivals, CPU usage, power, and thermal behavior. The model is accurate and avoids the calibration stage of RC thermal models. Second, based on this model, a linear programming problem (LPP) determines the existence of a feasible HRT thermal-aware schedule. Last, a sliding-mode controller and an online discretization algorithm implement the global HRT scheduler, which is capable of managing thermal constraints, context switching, migrations, and disturbances

Energy-efficient thermal-aware multiprocessor scheduling for real-time tasks using TCPNs

We present an energy-effcient thermal-aware real-time global scheduler for a set of hard real-time (HRT) tasks running on a multiprocessor system. This global scheduler fulfills the thermal and temporal constraints by handling two independent variables, the task allocation time and the selection of clock frequency. To achieve its goal, the proposed scheduler is split into two stages. An off-line stage, based on a deadline partitioning scheme, computes the cycles that the HRT tasks must run per deadline interval at the minimum clock frequency to save energy while honoring the temporal and thermal constraints, and computes the maximum frequency at which the system can run below the maximum temperature. Then, an on-line, event-driven stage performs global task allocation applying a Fixed-Priority Zero-Laxity policy, reducing the overhead of quantum-based or interval-based global schedulers. The on-line stage embodies an adaptive scheduler that accepts or rejects soft RT aperiodic tasks throttling CPU frequency to the upper lowest available one to minimize power consumption while meeting time and thermal constraints. This approach leverages the best of two worlds: the off-line stage computes an ideal discrete HRT multiprocessor schedule, while the on-line stage manage soft real-time aperiodic tasks with minimum power consumption and maximum CPU utilization

Modeling and Stability Analysis of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms

Computer control systems for safety critical systems are designed to be fault tolerant and reliable, however, soft errors triggered by harsh environments can affect the performance of these control systems. The soft errors of interest which occur randomly, are nondestructive and introduce a failure that lasts a random duration. To minimize the effect of these errors, safety critical systems with error recovery mechanisms are being investigated. The main goals of this dissertation are to develop modeling and analysis tools for sampled-data control systems that are implemented with such error recovery mechanisms. First, the mathematical model and the well-posedness of the stochastic model of the sampled-data system are presented. Then this mathematical model and the recovery logic are modeled as a dynamically colored Petri net (DCPN). For stability analysis, these systems are then converted into piecewise deterministic Markov processes (PDP). Using properties of a PDP and its relationship to discrete-time Markov chains, a stability theory is developed. In particular, mean square equivalence between the sampled-data and its associated discrete-time system is proved. Also conditions are given for stability in distribution to the delta Dirac measure and mean square stability for a linear sampled-data system with recovery logic

Modeling and analysis using hybrid Petri nets

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesi

Continuous flow Systems and Control Methodology Using Hybrid Petri nets

International audienceIn this paper, we consider the controller synthesis for continuous flow systems. These lasts are a sub-class of hybrid dynamic systems. Their main characteristics are positiveness and linearity. Transport, manufacturing, communication and biological systems are examples of continuous flow systems. Numerous tools and techniques exist in the literature for modelling and analyzing such systems. As positiveness is a hard constraint, an appropriate tool integrating naturally this constraint is strongly needed. Hybrid Petri Nets are an elegant modeling tool of positive systems, while Hybrid Automata are a powerful tool giving formally the reachable dynamic space. Combining these two tools aim to a sound approach for control synthesis of continuous flow systems. We start by considering the process to control and compute its reachable state space using specialized software like PHAVer. Algebraic inequalities define this reachable state space. The constrained behaviour is obtained by restricting this state space into a smaller desired space. This reduction is expressed in term of linear constraints only over the continuous variables; while the control is given by the discrete transitions (occurrence dates of controllable events). The controller synthesis methodology is based on the control of a hybrid system modelled by a D-elementary hybrid Petri Net. The control consists in modifying the guard of the controllable transitions so as the reachable controlled state space is maximally permissive