A framework is introduced for monitoring the interrupting faults in the timed discrete events systems. We introduce the notion of acceptable behavior of the system subjected to these faults: permanent or intermittent. The acceptable behavior of a system is modeled by a stopwatch automaton. The timed sub-spaces in the locations of the automaton delimit exactly the range of the acceptable behavior. They are synthesized using the techniques of reachability analysis of stopwatch automata in a way to detect the system faults as early as possible.

This paper extends the notion of residuals for fault detection, well known in the continuous system to the timed discrete events systems. The aim is to design the fault indicators, two problems are considered. Firstly, the dynamics of clocks which monitor the system must be sensible to the behavior change resulting from a fault. Secondly, we must specify the inequality clocks constraints for which the system is normal as long as they are satisfied. We introduce the notion of acceptable system behavior modeled by stopwatch automata. This behavior is supervised by two clocks for each interruptible task of the system. The time sub-spaces in the stopwatch automaton locations delimit exactly the range of acceptable behavior. They are synthesized using an algorithm based on the reachability analysis techniques of stopwatch automata. One of the main results of designing this time space is the detection the system faults as early as possible.

Summary form only given. The current expansion of communication networks offer services for private individuals in terms of access to information, communication between individuals, interactive play, as well as for economic or technical purposes such as banking applications, air traffic control, telerobotics, remote maintenance, medicine, etc. Data sent are converted into segments subjected to network constraints, namely delays, erroneous arrivals of messages or even loss of messages. With taking these constraints into consideration, our contribution is focused on network modeling, study of network dynamic behavior and of congestion avoidance. It is possible with this network modeling to determine the influence of communication networks on the transmission of control signals, since there are delays and losses induced by networks. This paper presents the modeling of a communication line in Internet environment under TCP/IP protocol. The behavior of the communication line is modeled as a continuous system (message flows); it is a satisfactory approximation. The behavior of the TCP protocols is seen as a discrete event system model. In this case, the global model is hybrid. We have chosen hybrid PNs as a unique modeling tool, since it gives accurate models of the complex functions found in Internet connections.

Hybrid systems have received much attention and a number of different models have been proposed in order to establish a mathematical framework which is able to handle both continuous and discrete aspects. Our research is focused on two models: hybrid automata and hybrid Petri nets (hybrid PNs). First, we deal with studying the hybrid PN functioning. An algorithm is proposed for constructing the hybrid automaton associated with a given hybrid PN. Next, we present the quantitative analysis of hybrid systems modeled by hybrid PN. The approach uses the reachability analysis of hybrid automaton to characterize the periodic functioning of a hybrid PN.

Synchronous systems can be distributed using different schemes of distribution. One possible distribution scheme is transforming the synchronous systems into a globally asynchronous locally synchronous system in which each site behaves synchronously while the exchanges between sites are asynchronous; this is a case of synchronous distributed systems. However, the obtained synchronous distributed system will present some bad behaviors due to delays introduced by the partial asynchronous behavior. Thus, we introduce order-insensitivity by analogy with delay-insensitivity of asynchronous hardware in order to have the same behavior in distributed and centralized implementations. This property characterizes systems where the parallel execution is equivalent to all possible sequential executions. Moreover, this property is not an intrinsic property to the state machine but only of its implementation. Consequently, we propose an algorithm for transforming an order-sensitive transition function into an equivalent order-insensitive one.

In synchronous systems, new asynchronous distribution schemes are introduced. Properties can be established in order to distribute a program with weak synchronization. This paper deals with automatic verification of the order-insensitive property. Order-insensitivity is an important property introduced in synchronous systems by analogy with delay-insensitivity in asynchronous hardware. An algorithm derived from the Eichelberger ternary algorithm in combinational and sequential switching circuits is given. The new ternary algorithm allows exact detection of order-insensitive property violation. Binary analyses which are conceptually simple and natural, can solve the verification of the order-insensitive property. However, this technique is exponential in the number of state variable computations. By analogy with asynchronous systems, ternary techniques are polynomial in the number of state variable computations. Our goal is to verify if a transition function describing a synchronous program is order-insensitive. Thus, the introduction of an uncertain value in addition to Boolean values allows concretization of the insensitivity introduced by the chaotic order of state variables processing in a distributed way (sequential processing).

This paper outlines some preliminary work on the analysis of continuous coupled linear hybrid systems. We introduce the time invariant linear hybrid automaton. We establish an analytic formulation of its steady state behavior for the case where the discrete structure is a cycle. We obtain the "clock translation" basis for this case. Finally, we show our preliminary work on the existence and uniqueness conditions of the steady state in the noncoupled case.

Two continuous Petri net (CPN) models involving time are defined. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The first model considers constant firing speeds (constant-speed CPN, CCPN). It is very easy to simulate. The second model considers firing speeds depending on the marking (variable speed CPN, VCPN). It provides a better approximation, but its simulation is longer because the markings and speeds are given by differential equations. The authors introduce a third model, which has the advantages of the two preceding ones. This model represents the asymptotic behavior of the VCPN. Their precision is similar. It is as easy to simulate as the CCPN.>

Continuous Petri nets (PNs) are presented, and continuous PN behavior is compared with the referential model (timed PN). A criterion is proposed to evaluate the approximation given by the continuous PN. The validity of this model is justified by comparison with the referential model (timed PN). This comparison permits the validation of the continuous model. The application of this tool for studying the dynamic behavior of manufacturing lines is discussed. Some properties of such lines are pointed out and then demonstrated using the analytical capacities of the continuous PN.>