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This paper addresses the problem of control design for T-Timed Discrete Petri Net (T-TDPN) systems. The problem is studied using Model Predictive Control (MPC) and Timed Continuous Petri Net (TCPN) systems. Our goal is to find an approach which determines, in a systematic way, the firing sequence that drives a T-TDPN from an initial marking to a desired one. Since it had been proved that the MPC is an attractive feedback strategy in the case of TCPN under infinite server semantics and that this latter represents a good fluid approximation of the Discrete Event Systems, the proposed method deals with MPC applied on the TCPN equivalent to the discrete one and then, from the obtained results, deduces the firing sequence and computes the discrete markings.

Liveness is a significant behavioral property of a Petri net. Siphons, as structural objects, are closely related to the liveness of a Petri net. For generalized systems of simple sequential processes with resources (GS3PR), a mixed integer programming (MIP) model is formulated, which can detect the existence of minimal non-max*-marked siphons that cause deadlocks or livelocks. We conclude that a GS3PR is live if there is no feasible solution to the formulated MIP model. An example is used to illustrate the proposed method.

In the framework of discrete event systems, the observation of events is considered as outputs in most problem settings, such as state estimation and fault diagnosis, while only a few studies exploit the availability of partial state information. In this paper, equivalent relations between Petri nets with different observation structures, i.e., Petri net generators, are discussed. We focus on a model called labeled Petri nets with outputs (LPNO), i.e., labeled Petri nets endowed with an arbitrary observation function of the marking. It has been shown that any LPNO can be converted into an adaptive labeled Petri net (ALPN) whose labeling function depends on the markings, if infinite labels are allowed. We propose an algorithm that converts a bounded LPNO into an equivalent ALPN with minimal alphabet, i.e., an alphabet of minimal cardinality, to avoid introducing a large number of unnecessary labels.

In this paper we study the problem of supervisory design using Petri nets. We consider a monolithic supervisor candidate, i.e., a net obtained by concurrent composition of plant and specification, and we say that the control problem has an OR-AND GMEC solution if the set of the legal markings of such a net can be described by a disjunction/conjunctions of linear constraints. We derive some sufficient conditions, based on the boundedness of some places of the net, for the existence of such a solution.

In this paper we study the problem of constraint transformation. We consider a special type of system in which the uncontrollable subnet is an assembly flow system, which is a subclass of backward-synchronization-backward-conflict-free Petri net. We propose an algorithm to transform a given inadmissable GMEC into an equivalent admissible OR-GMEC. The algorithm is based on a technique that adds new constraints obtained by composition of elementary ones.

This article concerns fault diagnosis for stochastic discrete event systems. For this purpose, partially observed stochastic Petri nets are introduced that include (i) the Markovian stochastic dynamics used to represent failure processes and also (ii) the model of the sensors used to measure the events and markings. Timed observation sequences result from this modeling and the probabilities of marking trajectories consistent with a given timed observation sequence are systematically computed. Diagnosis in terms of faults probability is obtained as a consequence and an algorithm of linear complexity is proposed to evaluate the fault probability on the basis of segments extracted from the timed observation sequence. Performance of the algorithm is discussed wrt to usual non detection and false alarm rates.

This paper presents a performance-regulation method for a class of Discrete Event Dynamic Systems (DEDS). The main idea is to use an integral controller with a variable gain, adaptively computed so as to guarantee effective output-tracking of a given reference value. The computation of the gain is based on the Infinitesimal Perturbation Analysis (IPA) gradient of the plant function with respect to the control variable, and the resultant tracking can be quite robust with respect to modeling inaccuracies and gradient-estimation errors. The proposed technique is tested on two examples concerning the regulation of the loss rate in a queue, and of inventory levels in a manufacturing-system represented by a Petri net. The results suggest its potential efficacy for a broader class of DEDS.

Hybrid Petri nets are known to be a powerful tool for modeling positive hybrid dynamic systems; and hybrid automata to have a great analysis power. Many authors have used these two models in a coupled manner to combine their advantages and translation algorithms from hybrid Petri nets to hybrid automata exist in the literature. Here we investigate a subclass of hybrid Petri nets called D-elementary hybrid Petri net. We present a structural algorithm allowing the translation of the D-elementary hybrid Petri nets out of linear hybrid automata. The resulting automaton has particular characteristics. The translation algorithm preserves the behavioral semantics; we prove hereafter the timed bisimilarity of the D-elementary hybrid Petri net and the linear hybrid automaton obtained by the translation algorithm. A manufacturing system will be used as an illustrative example.

This paper deals with Batches Petri nets and traffic road systems. To evaluate bottlenecks of traffic flows and control strategies, a first hybrid model at the mesoscopic level has been proposed based on Batches Petri nets with controllable batch speed. In this paper, this formalism is extended in order to represent the fundamental diagram as a triangular form, one of the three basic concepts of traffic dynamics. The batch place is enriched by a critical density and by a new comportment dedicated to the bottleneck behavior. Illustrated on a motorway example, the proposed batch formalism allows the traffic flow to be represented through hybrid and discrete event dynamics.

This paper addresses the problem of checking diagnosability of supervision patterns in discrete-event systems. With a supervision pattern, it is possible to represent a complex behavior of the system, and especially a faulty behavior. As opposed to classical diagnosability analyzers that check by exploring the marking graph of the underlying net, the proposed method relies on Petri net unfoldings and thus avoids the combinatorial explosion induced by the use of marking graphs. The method is an adaptation of the twin-plant method to net unfolding: a pattern is diagnosable if the unfolding representing the twin-plant does not implicitly contain infinite sequences of events that are ambiguous.

International audience; Integrated Deterministic and Probabilistic Dependability Analysis (IDPDA) is respectively required for safety properties veri cation and reliability & availability assessment of critical systems. This paper presents an approach towards IDPDA using Coloured Petri Nets (CPN). Contributions are related to: (a) hierarchical modelling guidelines that cover deterministic and probabilistic features of a physical system under control, (b) coupling Monte-Carlo simulation with CPN model checking that requires a previous determinisation of the CPN stochastic model. Our approach is illustrated using a toy case study.

This paper aims to present P-Temporal Petri Net models for a specific kind of real industrial problems. This class of problems is known in the literature as CHSP, Cyclic Hoist Scheduling Problem. Several jobs have to flow through a production line according to an ordered bath sequence. Firstly, they enter the line from a loading buffer. Then, they will be soaked sequentially in a series of tanks containing specific chemical baths. Finally, they will leave the line at the unloading buffer. The processing time duration of each job in each tank is not constant but confined in a time interval. Moreover the transport of jobs between tanks is insured by a transport resource called hoist. In this paper, we propose a linear programming model to determine an optimal production plan of the studied system while determining the exact beginning and ending instants of each task. The second contribution of the paper is to propose P-Temporal Petri net models describing the behavior of many configurations of the production line. The proposed modeling approach enables to describe the system and validate its qualitative properties using the simulation tool Visual Object Net ++.

In this paper a method is proposed for preventing the system from entering the forbidden states in Discrete Event Systems. So, a small number of control places are obtained by solving a few integer linear programming problems. The numbers of constraints and variables in each problem linearly grow with respect to the number of authorized states and forbidden states. The controller after connecting the obtained control places to the model is maximally permissive.

Deterministic and stochastic Petri nets (DSPNs) are well utilized as a visual and mathematical formalism to model discrete event systems. This paper proposes to use them to model parallel railroad level crossing control systems. Their applications to both single and double-track railroad lines are illustrated. The resulting models allow one to identify and thus avoid critical scenarios in such systems by conditions and events of the model that control the phase of traffic light alternations. Their analysis is performed to demonstrate how the models enforce the phase of traffic transitions by a reachability graph method. Their important properties are verified. In this paper, we employ DSPNs to model a parallel railroad level crossing system and identify its critical scenarios for the purpose of their complete avoidance. This helps advance the state-of-the-art in traffic safety related to the intersection of railroads and roadways.

Petri nets are suitable for modelling of discrete-event systems with highly parallel and cooperating activities. In complex man-made systems, such as manufacturing systems, the systems' specific properties, such as conflicts, deadlocks, limited buffer sizes, and finite resource constraints can be easily represented in the Petri net model. Therefore teaching of Petri net basics is an inevitable component of courses on modelling and simulation. The paper presents an object oriented Matlab m-script based Petri net tool, which is used to implement Petri net examples within MMT-server e-learning environment. The tool structure is described, and basic examples on timed Petri net simulation and simulation-based optimization of schedules are provided.

We show that the predictability problem for a Petri net can be reduced to LTL-X model checking. The advantage of this is that existing efficient methods and tools can be employed, in particular parallel model checking based on Petri net unfoldings. The experimental results show that this approach is efficient, and a good level of parallelisation can be achieved.

The deadlock control and liveness-enforcement are mostly implemented based on siphons in most existing work using structural theory. Our previous work has revealed a kind of intrinsically live structures in a class of generalized Petri nets called systems of simple sequential processes with weighted resources allocation (WS 3 PR). The liveness-enforcement is achieved by analyzing the structure including weight information and reconfiguring the initial marking of resource places without considering the initial token counts in idle process places. This work extends it to a more general class than WS 3 PR. Instead of siphons, a new concept of structural objects is defined to carry weight information and reflect the circular waits of resources. The numerical relationship between initial markings of resource places and weights of arcs is investigated to yield an intrinsically live structure-based liveness-enforcing method that requires no external monitors. The work provides an insight into structures of generalized Petri nets and a new revenue to achieve the desired deadlock control. Several examples are used to illustrate the proposed method.

A novel method for discrete event systems described by Petri nets are proposed in this paper for model-based diagnosis. The model of the investigated system was defined in hierarchical colored CP-net form. Both normal reference model describing the faultless operation and the extended model containing the different faults were developed. For the fault simulation we used the arc and transition inscriptions. In order to visualize the model in different faulty modes a converter program were developed. The proposed procedure was illustrated on a simple manufacturing process with different faulty modes.

In this paper we consider controlled Generalised Batches Petri Nets, a class of batches nets where the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables to be selected within an admissible range. We show that the steady state behavior of this class of nets during a period in which no discrete transition fires can be characterized by solving a nonlinear programming problem that takes into account the net structure and the initial marking. A viable technique to compute a family of solutions by linear relaxation is also presented.

This paper studies the problem of optimal static sensor selection for ensuring diagnosability in labeled bounded Petri nets. Starting from a non-diagnosable labeled Petri net system, we present a systematic procedure to design a new labeling function that makes the system diagnosable and optimizes a given objective function. This procedure employs a particular net, called Verifier Net, that is built from the original Petri net and provides necessary and sufficient conditions for diagnosability. We exploit the system structure captured in the verifier net to guide the search for the desired new labeling function. The search is performed over an unfolding of the reachability tree of the verifier net.

Controllability of timed continuous Petri nets (TCPN) is studied in this work. The analysis addressed here may lead to control algorithms for systems modeled with TCPNs, for instance, manufacturing systems, supply chains, etc. The goal in this work is to provide structural and generic conditions for the verification of the controllability property. In particular, it is proven that for the net subclass of Topological Equal Conflict net systems the controllability may be determined by the structure, being independent of the timing of the transitions.

In the domain of discrete event systems, various approaches have been developed for the detection and diagnosis of faults. This paper concerns the fault detection and diagnosis with Petri nets according to a state-based approach that uses the properties of the reachability graph. The proposed method provides a decision thanks to the analysis of observation sequences that include the capture of some observable events and the partial measurement of the markings variation. For that purpose, elementary firing sequences are introduced and characterized with matrix linear inequalities (LMIs). Sufficient conditions for fault detection and diagnosis are stated as a consequence.

Symmetries in continuous Petri nets result in symmetric system behaviors. This fact is used by the method suggested in this contribution. We present a structured procedure to construct a Petri net of smaller size which has the same dynamical behavior as the original net. It consists of an automated construction of the reduced net including the adaption of arc weights and firing rates and works under mild assumptions on unequal conflicts.

Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Discrete Event Systems (DES). As most formalisms for DES, PNs suffer from the state explosion problem. A way to overcome this difficulty is t o relax the original discrete model and deal with a fully or partially continuous model. In contrast to continuous Petri nets that consider a full continuous firing of transitions, what can lead to the loss some properties of the original discrete model; this paper deals with Hybrid Adaptive Petri nets (HAPNs), that consider partially continuous firings. In an HAPN, a threshold is associated with each transition: if the load of the transition is higher than its threshold, it behaves as continuous; if it is lower, it behaves as discrete. This way, transitions adapt dynamically to their load. The reachability space and the deadlock-freeness property of HAPNs are studied and compared to those of discrete and continuous Petri nets.

In this paper we present a procedure to analyze the diagnosability of a Petri net system in a decentralized framework. We recall the denition of failure ambiguous strings, i.e., strings that can be both faulty or not in the decentralized case, while can be distinguished in a centralized framework. We rst prove that the absence of such kind of strings guarantees that the system is diagnosable in a decentralized framework. Then, we give an ecient procedure to verify the absence of such kind of strings for both bounded and unbounded Petri net systems. A computational complexity analysis of such procedure is also presented.

In this paper, we present an online algorithm for state estimation of timed choice-free Petri nets. We assume that the net structure and initial marking are known, and that the set of transitions is divided in observable and unobservable one. Given an observed word and assuming that the time durations associated to the unobservable transitions are unknown, our problem is to estimate the possible states in which the timed net system can be. This work extends the notion of basis markings defined for untimed Petri nets considering now the time information. The proposed algorithm deals with three main steps: (1) wait for a new observation and compute the set of basis markings without considering the time; (2) update the set of time equations that contain the time restriction for the unobservable transitions; (3) update the set of basis markings removing the time-inconsistent markings. The extension of the algorithm to general nets is discussed, as well.

This paper addresses the problem of optimal control in the context of ordinary Petri net (PN) models. The meaning and importance of both formal and structural PN control optimality is discussed. A novel approach, based on a spacial view of the system's state space, is used to determine control constraints that insure optimality. A simplification technique producing the minimal optimal control solution is proposed, and outlined in an algorithm. Finally, the approach is illustrated via an example.

This paper considers an application of the Infinitesimal Perturbation Analysis (IPA) gradient-estimation technique to a class of continuous Petri nets. In particular, it proposes a systematic approach for computing the derivatives of the sample performance functions with respect to structural and control parameters. The resulting algorithms are recursive in both time and network flows, and their steps are computed in response to the occurrence and propagation of certain events in the network. Such events correspond to discontinuities in the network flow-rates, and their special characteristics are due to the properties of continuous transitions and fluid places. Following a general outline of the framework we focus on a simple yet canonical example, and investigate throughput and workload-related performance criteria as functions of a threshold control variable. Simulation experiments support the analysis and testify to the potential viability of the proposed approach.

Stochastic hybrid systems represent established classes of realistic models of hybrid dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. In this paper, we tackle the stochastic reachability problem from a purely probabilistic perspective. Using the connection between stochastic reachability and optimal stopping, the reach probabilities are estimated using only the probabilistic parameters (transition probabilities, infinitesimal generator) of stochastic hybrid systems. The technique is illustrated first for Markov chains, then for other more complex Markov models.

In this paper 1-safe interval P-time Petri nets are described using linear description in an interval like idempotent semiring. This semiring, which is just the product of semirings Rmax and Rmin, enables linear letter driven description similar to the one known for timed Petri nets. Examples illustrating our approach show also an application of this description to dead token detection.

In this paper we consider Generalised Batches Petri nets (GBPN) and develop new linear algebraic techniques for the analysis of this model. Two main contributions are presented. The first contribution lies in the fact that although we consider the same GBPN model that has already be presented in the literature, we associate to this model a different semantics considering that the instantaneous firing flow of continuous and batch transitions are control variables that can take an arbitrary value provided they satisfy given constraints. The second contribution consists in the analysis of the steady state behavior of GBPN. We show that under the assumption that no discrete transition fires, a steady state can be characterized by solving a linear programming problem that takes into account the net structure and the initial marking.

Recently there has been a considerable interest in the application of Infinitesimal Perturbation Analysis (IPA) to continuous queues, where its sample derivatives (gradients) were shown to be unbiased for a large class of systems. This paper extends the investigation to a class of hybrid Petri nets, where the special algebraic structure of continuous transitions yields simple algorithms for the IPA derivatives. We derive such algorithms for the performance functions of throughput and average workload, and show them to be model-free and easily computable from the sample paths.

Reliability analysis is often based on stochastic discrete event models like stochastic Petri Nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. For this reason, fluidification is an interesting alternative to estimate the asymptotic behaviour of stochastic processes with continuous Petri nets. Unfortunately, the asymptotic mean marking of stochastic and continuous Petri nets with same structure and same initial marking are mainly often different. This paper shows that this difficulty is related to the partition in regions of the reachability state space. A geometric approach is developed to characterize the regions and to get a partial homothetic approximation of the stochastic steady state.

Quality regulation methodology was developed to control and improve the product and the performance evaluation in Discrete Event Systems (DES). The same particularity may be found on process where the associated constraints do not concern the time. Thus the objective of quality regulation system is to ensure that measure a product's quality fall into ranges that are acceptable to prospective customers. The control must guarantee the values of the quality variable may or may not fall a random pattern within the limits specified. So a suitable model, rich in analytical properties, is necessary to synthesize the needed controller. This paper proposes a modelling approach of regulation quality systems with temporal and non temporal constraints. A methodology of robust control construction generating the margins of robustness is being elaborated. The methodology is based on a hybrid Petri Nets: a new modelling tool the Interval Constrained Petri Nets (ICPN) in order to evaluate the variations of the quality of tobacco and P-time Petri Nets to manage the flow type disturbance.

Since its birth, about fifty years ago, the reliability field develops methods and tools to satisfy its different needs and this is more and more difficult as industrial systems becomes more and more complex and required parameters more and more sophisticated. Then the simplistic reliability and availability calculations of the origins are no longer sufficient to fulfill the present time needs encountered when dealing with RAM (Reliability, Availability, and Maintainability) or SIL (Safety Integrity Level) analysis. The dynamical behavioral aspects and the combinatory explosion of the number of states of industrial size system imply to proceed to a qualitative jump to be able to manage them properly. This may be done simply by moving from the traditional analytical approach to the Monte Carlo simulation. Nevertheless to be implemented efficiently this approach needs a powerful model behaving a close as possible as the physical system which is modeled. Finite states automata are generally chosen for this purpose and, among them the stochastic Petri nets (SPN) have proven to be very effective. This is the aim of this paper to show how SPN may be used for RAM (i.e. dependability) and SIL (i.e. functional safety) objectives.

Modern production systems are characterized by numerous conjoint and interacting production machines each with sophisticated maintenance and logistic processes. To remain competitive, it is necessary to reduce the system downtimes by applying the optimal maintenance strategy and therefore reducing life cycle costs. Condition monitoring often is a very effective way to minimize downtimes of crucial system components such as ball screws, ball bearings and drives. But sometimes condition monitoring is not cost-effective or even reduces the system's operational availability. The decision whether it's reasonable to implement condition based maintenance or not requires a detailed analysis of the system's behavior. Since many analytical models of technical systems have significant limitations and simplifications, simulation techniques are applied very often In our paper we will present an improved comprehensive methodology for the modeling and analysis of production systems which has been basically introduced at the RAMS-Symposium in 2008. The model incorporates an extended colored stochastic Petri net (ECSPN) and a reliability block diagram (RBD) in a conjoint modeling procedure which allows a close-to-reality representation of a complex production system's behavior.

In this paper, we present an algorithm for diagnosis issues in DES. Detection and isolation of faults are performed according to a time Petri net derived from a stochastic Petri net with normal distributions of the firing periods. This model is then extended in order to model fault and recovery processes. Faults characterization results as a consequence. Design and identification of the models parameters are detailed.

A Markovian Petri net is a stochastic discrete event system (DES) frequently used for analysis and performance evaluation purposes. In the past, the fluidification has been proposed in different DES's as a relaxation technique for avoiding the “state explosion problem”. Following the same approach, in this paper a hybrid Petri net model is defined as a partial relaxation of an original Markovian Petri net. It is shown through a simple example that such partial relaxation can be worse than a full relaxation (given by a fully continuous Petri net). Therefore, the rest of the paper is devoted to obtain sufficient conditions for guaranteeing the approximation of the hybrid Petri net model to the original discrete system.

The dynamics of timed continuous Petri nets under infinite server semantics can be expressed by a piecewise linear system with polyhedral regions. In this paper we establish connections between the qualitative behavior of the dynamics of the continuous marking and the net structure. In particular, Petri nets with symmetries are addressed where symmetry is understood as a permutation symmetry of the nodes. It is shown that such a symmetry leads to a permutation of the regions and equivariant dynamics.

Performance evaluation and reliability analysis for dynamical systems are often based on stochastic Petri net models. The synthesis of the model structure and the identification of the time parameters are difficult problems that must be investigated in order to build efficient models. In this paper, we propose an identification method based on the analysis of collected event sequences. This method is inspired from a numerical approach with an optimization algorithm. The advantage of this method is that it succeeds also for non markovian marking processes. As a consequence, it is suitable for the identification of stochastic Petri nets with normal or other random distributions of the firing periods. An example that combines normal and exponential distributions of the firing periods is proposed.

Reachability is one of the most important behavioral properties of Petri nets and the past four decades have witnessed great efforts in developing various implementable methodologies in determining reachability of Petri nets. We propose in this paper a novel method for solving the fundamental equation in the reachability analysis, which has been known to be NP-complete. More specifically, by adopting a revised version of the cell enumeration method for an arrangement of hyperplanes in discrete geometry, we develop an efficient solution scheme to identify firing count vector solution(s) to the fundamental equation on a bounded integer set, with a complexity bound of O (( n ω) n–m ), where n is the number of transitions, m is the number of places and ω is the upper bound of the number of firings for every transition.

Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. The contribution of this paper is to approximate the steady state of mono T-semiflow stochastic nets by mean of continuous Petri nets according to a modification of the maximal firing speed vector definition. This result is then used to accelerate convergence of stochastic simulations.

This paper shows the impact of the trade-off between reconfigurable and non-reconfigurable parts of the FPGA to the dependability characteristics of the whole design. Stochastic Petri nets have been used to compute reliability and dependability characteristics in a simple FPGA design with dynamically reconfigurable modules. Some parts of the design are not possible or proper to reconfigure dynamically (e.g. module interconnections, module-pin connections …). A non-reconfigurable overhead may have a significant effect to the availability of the design. The granularity of reconfigurable parts and their number can also affect dependability parameters. The method how to enumerate these effects via a formal dependability model is shown in this paper.

The paper deals with formal verification of parallel discrete systems, for which state explosion is a major problem. We consider the Petri net models of parallel logical control algorithms. Such algorithms can usually be modeled by Petri nets belonging to specific classes. We propose two methods of verification of Petri nets by means of constructing reduced reachability graphs. First of them uses the stubborn sets and allows to decide well-formedness of the Petri nets having structures typical for control algorithms, and hence to verify such algorithms automatically. Second one allows to detect deadlocks of ordinary Petri nets by concurrent simulation, often reducing state spaces deeper than the first method.

Int. Fed. Autom. Control (IFAC) - Tech. Comm.;Comput. Control;Int. Fed. Autom. Control (IFAC) - Tech. Comm.;Discrete Event Hybrid Syst.;Technical Committe 2.1 on Control Design;Technical Committe 3.2 on Computational Intelligence in Control, 4th IFAC Workshop on Discrete-Event System Design, DESDes'09 -- 6 October 2009 through 8 October 2009 -- Gandia -- 85833, Unlike untimed Petri nets, representation of the state of a timed Petri net and describing its evolution is not an easy task. Here, an approach, called place-stretching, is introduced to represent the state of a timed-place Petri net. This approach also facilitates the description of the evolution of the state of a timed-place Petri net. An algorithm, which uses this approach, to construct the reachability set of a timed-place Petri net is also developed. An example is also presented to demonstrate the introduced approach and the usage of the developed algorithm.

This paper deals with the use of Petri nets in a specific class of scheduling issues. Indeed, in a specific type of one machine problems, the job processing time is not any more constant but depend on time. When the temporal functions representing the evolution of the processing time of the tasks are polynomial functions, the problems are difficult to resolve in certain cases. We propose an algorithm which is validated by a Petri net model to give a feasible solution.

International audience; The purpose of the paper is to illustrate a method, based on scenario deriving, to address dynamic reliability of hybrid systems. Petri nets are used to model the discrete aspects and di®erential equations for the continuous ones. The discrete aspects are addressed by a Petri net player based on linear logic and the continuous one by simulating the di®erential equations. These two simulators (Petri net player and simulator of di®erential equations) evolve alternatively and communicate between them. The originality of the approach resides in its local character. Indeed, only the interesting part of the model from reliability point view is simulated.

Timed continuous Petri net systems with infinite server semantics are piecewise linear systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and measuring some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable configurations is introduced. It helps to give a necessary and sufficient criterion for the observability in infinitesimal time. Using results from linear structured systems (Commault et al. (2005)), the concept of generic observability is introduced and it is studied in the case of join free nets.

The paper addresses the fault detection problem for discrete event systems on the basis of a Petri Net (PN) model. Assuming that the structure of the PN and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions that are associated with the system legal behaviour and that the marking reached after the firing of a transition is unknown. We propose a diagnoser that works on-line: it waits for the firing of an observable transition and employs an algorithm based on the definition of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults.