The diagnosis of discrete event systems is strongly related to events estimation. This paper focuses on faulty behaviors modeled with ordinary Petri nets with some "fault" transitions. Partial but unbiased measurement of the places marking variation is used in order to estimate the firing sequences. The main contribution is to decide which sets of places must be observed for the exact estimation of some given firing sequences. Minimal diagnosers are defined that detect and isolate the firing of fault transitions immediately. Causality relationships and directed paths are also investigated to characterize the influence and dependence areas of the fault transitions. Delayed diagnosers are obtained as a consequence. Note to Practitioners-Structural tools are provided for the analysis of models used in the context of fault detection and isolation for discrete event systems. The systems that are concerned are either manufacturing processes, batch processes, digital devices, or communication protocols with single or multiple failures. Methods are proposed to decide, in a systematic way, if the considered failures can be detected and isolated according to the existing sensors. The obtained results can also be used by designers for sensor selection

Petri nets are a suitable tool for the modeling, analysis, and control design of hybrid systems because they offer the opportunity to combine discrete dynamics with continuous ones in a comprehensive way. This paper is about the structural sensitivity of the nodes (places or transitions) with respect to the firing and staying conditions attached to the Petri nets. The sensitivity of subnets is also concerned. The proposed results are interesting to decide if the marking of a given place or the firing sequence of a given transition depends or not on the value of a given parameter that is attached to a particular node or subnet. Conflicts are considered as a particular class of subnets. As a consequence, the structural sensitivity provides some information about the influence and dependence areas of conflicts.

The paper presents a new technique to infer 3D information using a static camera provided with a zoom lens. The modelling process is straightforward and does not involve the computation of intrinsic camera parameters. The approach is based on the exploitation of images of accurate regular grids. The main idea is to compute a transformation which allows to obtain a relationship between the real grids (without distortion) located in front of the camera and their distorted images on the CCD matrix. This relationship takes automatically all the distortion phenomena into account. Previous work in reconstruction by zooming involved high quality optical systems. The principal aim of the present work is to generalize this kind of reconstruction in the case of a standard zoom lens.>