Edouard Leclercq

Stochastic Petri Net Identification for the Fault Detection and Isolation of Discrete Event Systems

This paper is about fault detection and identification of discrete event systems. The proposed approach is based on Petri nets (PNs) that are used to design reference and faulty models. The main contribution concerns the design and identification of these models according to the statistical analysis of the alarm sequences that are collected on the considered system. The model structure is described as a state graph, and the parameters of the probability density functions (pdfs) for transition firing periods are estimated. Normal and exponential pdfs are considered, and estimation is detailed in case of concurring behaviors. The reference models, described as timed PNs, are then used for fault detection and isolation issues. Finally, stochastic PNs with normal and exponential pdfs are considered to include a representation of the faulty behaviors.

Autonomous learning algorithm for fully connected recurrent networks

In this paper, fully connected RTRL neural networks are studied. In order to learn dynamical behaviours of continuous time processes or to predict numerical time series, an autonomous learning algorithm has been developed. The originality of this method consists in the gradient-based adaptation of the learning rate and time parameter of neurons using a small perturbations method. Starting from zero initial conditions (neural states, rate of learning, time parameter and matrix of weights) the evolution is completely driven by the dynamic of the learning data. Stability issues are discussed, and several examples are investigated in order to compare the performances of the adaptive learning rate and time parameter algorithm with the constant parameters one.

Control Design for Trajectory Tracking With Untimed Petri Nets

This technical note is about trajectory tracking for discrete event systems. The main contribution is to compute incrementally control sequences with minimal or near-minimal length based on a partial exploration of the Petri net (PN) reachability graph and inspired by the model predictive control approach. The method is suitable for bounded and unbounded PNs, for PNs with weighted arcs and with some uncontrollable transitions. Finally forbidden markings or regions of markings are easily avoided with the proposed approach that can be used for supervisory control issues.

Design and Identification of Stochastic and Deterministic Stochastic Petri Nets

In this paper, we consider the identification problem of stochastic and deterministic stochastic Petri nets (PNs). The approach herein proposed consists of inferring a PN structure and identifying its parameters. Hence, the first step leads to the synthesis of a PN structure with the measurable sequence of events and states. This approach determines the measurable part and estimates the nonmeasurable part of the PN to be established. Once both parts are obtained, the PN structure and the initial marking of the nonmeasurable places are obtained thanks to the integer linear programming technique. In the second step of this approach, the parameters of the obtained model are estimated. Stochastic and deterministic stochastic PNs with deterministic and exponentially distributed transition durations are considered. A systematic identification method is proposed based on event sequences that are recorded by supervision systems. This method is based on a Markov model whose state space is isomorphic to the reachability graph of the untimed PN model.

Piecewise constant timed continuous PNs for the steady state estimation of stochastic PNs

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 computation of numerical approximations is also time consuming due to the slow convergence of stochastic simulations. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes. The contributions of this paper are to point out that timed continuous Petri nets may lead to biased estimators of the stochastic steady state and to introduce fluid Petri nets with piecewise-constant maximal firing speeds and sufficient conditions in order to obtain unbiased estimators.

Indirect neural control for plant-wide systems: Application to the Tennessee Eastman Challenge Process

Abstract An autonomous indirect scheme is proposed for multivariable process control and is extended to unstable open-loop plant-wide processes. Our principal objective in this work is to prove the feasibility to control an industrial plant by a small size neural system without any a priori training. The control scheme is made of an adaptive instantaneous neural model, a Neural Controller based on fully connected “Real-Time Recurrent Learning” networks and an on-line parameters updating law. This control scheme is applied to the Tennessee Eastman Challenge Process. Performances such as set point stabilisation, mode switching and disturbances rejection are pointed out. Results are discussed according to the Down and Vogel control objectives.

Faults prognosis using partially observed stochastic Petri nets

This article deals with the problem of fault prognosis in stochastic discrete event systems. For that purpose, partially observed stochastic Petri nets are considered to model the system with its sensors. The model represents both healthy and faulty behaviors of the system. Marking trajectories which are consistent with the measurements issued from the sensors are first obtained. Based on the events dates, the probabilities of the consistent trajectories are evaluated and a state estimation is obtained as a consequence. From the set of possible current states and their probabilities, a method to evaluate the probability of future fault is developed using a probabilistic model. An example is presented to illustrate the results.

Feasibility of piecewise-constant control sequences for timed continuous Petri nets

In this study, the determination of control actions for timed continuous Petri nets is investigated by the characterisation of attractive regions in marking space. In particular, attraction in finite time, which is important for practical issues, is considered. Based on the characterisation of attractive regions, the domain of admissible piecewise constant control actions is computed, and sufficient conditions to verify the feasibility of the control objectives are proposed. As a consequence, an iterative procedure is presented to compute piecewise constant control actions that correspond to local minimum time control for timed continuous Petri nets.

Control design for contPN with piecewise-constant maximal firing speeds

Abstract Fluidification of Petri nets (PNs) has been used for the control design of discrete event systems. Timed continuous Petri nets with infinite server semantic (contPNs) have been used for that purpose as long as such models provide an acceptable approximation of the average discrete behaviours in long run. Newertheless, the convergence to a desired steady state is not trivial with contPNs. In this paper, timed continuous PNs with piecewise-constant maximal firing speeds are introduced for the marking regulation and sufficient conditions for the existence of a steady state are proposed in forced regime. The approach is based on the partition of the marking space into several regions.

Gradient-based controllers for timed continuous Petri nets

This paper is about control design for timed continuous Petri nets that are described as piecewise affine systems. In this context, the marking vector is considered as the state space vector, weighted marking of place subsets are defined as the model outputs and the model inputs correspond to multiplicative control actions that slow down the firing rate of some controllable transitions. Structural and functional sensitivity of the outputs with respect to the inputs are discussed in terms of Petri nets. Then, gradient-based controllers (GBC) are developed in order to adapt the control actions of the controllable transitions according to desired trajectories of the outputs.