Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR–AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach

Decomposition of sequential and concurrent models

Le macchine a stati finiti (FSM), sistemi di transizioni (TS) e le reti di Petri (PN) sono importanti modelli formali per la progettazione di sistemi. Un problema fodamentale è la conversione da un modello all'altro. Questa tesi esplora il mondo delle reti di Petri e della decomposizione di sistemi di transizioni. Per quanto riguarda la decomposizione dei sistemi di transizioni, la teoria delle regioni rappresenta la colonna portante dell'intero processo di decomposizione, mirato soprattutto a decomposizioni che utilizzano due sottoclassi delle reti di Petri: macchine a stati e reti di Petri a scelta libera. Nella tesi si dimostra che una proprietà chiamata ``chiusura rispetto all'eccitazione" (excitation-closure) è sufficiente per produrre un insieme di reti di Petri la cui sincronizzazione è bisimile al sistema di transizioni (o rete di Petri di partenza, se la decomposizione parte da una rete di Petri), dimostrando costruttivamente l'esistenza di una bisimulazione. Inoltre, è stato implementato un software che esegue la decomposizione dei sistemi di transizioni, per rafforzare i risultati teorici con dati sperimentali sistematici. Nella seconda parte della dissertazione si analizza un nuovo modello chiamato MSFSM, che rappresenta un insieme di FSM sincronizzate da due primitive specifiche (Wait State - Stato d'Attesa e Transition Barrier - Barriera di Transizione). Tale modello trova un utilizzo significativo nella sintesi di circuiti sincroni a partire da reti di Petri a scelta libera. In particolare vengono identificati degli errori nell'approccio originale, fornendo delle correzioni.Finite State Machines (FSMs), transition systems (TSs) and Petri nets (PNs) are important models of computation ubiquitous in formal methods for modeling systems. Important problems involve the transition from one model to another. This thesis explores Petri nets, transition systems and Finite State Machines decomposition and optimization. The first part addresses decomposition of transition systems and Petri nets, based on the theory of regions, representing them by means of restricted PNs, e.g., State Machines (SMs) and Free-choice Petri nets (FCPNs). We show that the property called ``excitation-closure" is sufficient to produce a set of synchronized Petri nets bisimilar to the original transition system or to the initial Petri net (if the decomposition starts from a PN), proving by construction the existence of a bisimulation. Furthermore, we implemented a software performing the decomposition of transition systems, and reported extensive experiments. The second part of the dissertation discusses Multiple Synchronized Finite State Machines (MSFSMs) specifying a set of FSMs synchronized by specific primitives: Wait State and Transition Barrier. It introduces a method for converting Petri nets into synchronous circuits using MSFSM, identifies errors in the initial approach, and provides corrections

Controller synthesis for parameterized discrete event systems

Les systèmes à événements discrets sont des systèmes dynamiques particuliers. Ils changent d’état de fa¸con discrète et le terme événement est utilisé afin de représenter l’occurrence de changements discontinus. Ces systèmes sont principalement construits par l’homme et on les retrouve surtout dans les secteurs manufacturier, de la circu- lation automobile, des bases de données et des protocoles de communication. Cette thèse s’intéresse au contrôle des systèmes paramétrés à événements discrets où les spécifications sont exprimées à l’aide de prédicats et satisfont une condition de similarité. Des conditions sont données afin de déduire des propriétés, en observation partielle ou totale, pour un système composé de n processus similaires à partir d’un système com- posé de n0 processus, avec n ≥ n0. De plus, il est montré comment inférer des politiques de contrôle en présence de relations d’interconnexion entre les processus. Cette étude est principalement motivée par la faiblesse des méthodes actuelles de synthèse pour le traitement des problèmes industriels de taille réelle.Discrete event systems are a special type of dynamic systems. The state of these systems changes only at discrete instants of time and the term event is used to represent the occurrence of discontinuous changes. These systems are mostly man-made and arise in the domains of manufacturing systems, traffic systems, database management systems and communication protocols. This thesis investigates the control of parameterized discrete event systems when specifications are given in terms of predicates and satisfy a similarity assumption. For systems consisting of similar processes under total or partial observation, conditions are given to deduce properties of a system of n processes from properties of a system of n0 processes, with n ≥ n0. Furthermore, it is shown how to infer a control policy for the former from the latter’s, while taking into account interconnections between processes. This study is motivated by a weakness in current synthesis methods that do not scale well to huge systems

An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S 4 PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons are max -controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S 4 PR is established

Timing analysis of synchronous data flow graphs

Consumer electronic systems are getting more and more complex. Consequently, their design is getting more complicated. Typical systems built today are made of different subsystems that work in parallel in order to meet the functional re- quirements of the demanded applications. The types of applications running on such systems usually have inherent timing constraints which should be realized by the system. The analysis of timing guarantees for parallel systems is not a straightforward task. One important category of applications in consumer electronic devices are multimedia applications such as an MP3 player and an MPEG decoder/encoder. Predictable design is the prominent way of simultaneously managing the design complexity of these systems and providing timing guarantees. Timing guarantees cannot be obtained without using analyzable models of computation. Data flow models proved to be a suitable means for modeling and analysis of multimedia applications. Synchronous Data Flow Graphs (SDFGs) is a data flow model of computation that is traditionally used in the domain of Digital Signal Processing (DSP) platforms. Owing to the structural similarity between DSP and multimedia applications, SDFGs are suitable for modeling multimedia applications as well. Besides, various performance metrics can be analyzed using SDFGs. In fact, the combination of expressivity and analysis potential makes SDFGs very interesting in the domain of multimedia applications. This thesis contributes to SDFG analysis. We propose necessary and sufficient conditions to analyze the integrity of SDFGs and we provide techniques to capture prominent performance metrics, namely, throughput and latency. These perfor- mance metrics together with the mentioned sanity checks (conditions) build an appropriate basis for the analysis of the timing behavior of modeled applications. An SDFG is a graph with actors as vertices and channels as edges. Actors represent basic parts of an application which need to be executed. Channels represent data dependencies between actors. Streaming applications essentially continue their execution indefinitely. Therefore, one of the key properties of an SDFG which models such an application is liveness, i.e., whether all actors can run infinitely often. For example, one is usually not interested in a system which completely or partially deadlocks. Another elementary requirement known as boundedness, is whether an implementation of an SDFG is feasible using a lim- ited amount of memory. Necessary and sufficient conditions for liveness and the different types of boundedness are given, as well as algorithms for checking those conditions. Throughput analysis of SDFGs is an important step for verifying throughput requirements of concurrent real-time applications, for instance within design-space exploration activities. In fact, the main reason that SDFGs are used for mod- eling multimedia applications is analysis of the worst-case throughput, as it is essential for providing timing guarantees. Analysis of SDFGs can be hard, since the worst-case complexity of analysis algorithms is often high. This is also true for throughput analysis. In particular, many algorithms involve a conversion to another kind of data flow graph, namely, a homogenous data flow graph, whose size can be exponentially larger than the size of the original graph and in practice often is much larger. The thesis presents a method for throughput analysis of SD- FGs which is based on explicit state-space exploration, avoiding the mentioned conversion. The method, despite its worst-case complexity, works well in practice, while existing methods often fail. Since the state-space exploration method is akin to the simulation of the graph, the result can be easily obtained as a byproduct in existing simulation tools. In various contexts, such as design-space exploration or run-time reconfigu- ration, many throughput computations are required for varying actor execution times. The computations need to be fast because typically very limited resources or time can be dedicated to the analysis. In this thesis, we present methods to compute throughput of an SDFG where execution times of actors can be param- eters. As a result, the throughput of these graphs is obtained in the form of a function of these parameters. Calculation of throughput for different actor exe- cution times is then merely an evaluation of this function for specific parameter values, which is much faster than the standard throughput analysis. Although throughput is a very useful performance indicator for concurrent real-time applications, another important metric is latency. Especially for appli- cations such as video conferencing, telephony and games, latency beyond a certain limit cannot be tolerated. The final contribution of this thesis is an algorithm to determine the minimal achievable latency, providing an execution scheme for executing an SDFG with this latency. In addition, a heuristic is proposed for optimizing latency under a throughput constraint. This heuristic gives optimal latency and throughput results in most cases

Formal techniques for the procedural control of industrial processes

Imperial Users onl