A. El Moudni

Continuous Petri nets models for the analysis of traffic urban networks

The traffic flow theory is concerned with finding a relation among the variables of traffic flow. We propose a new approach which consists of representing these variables by those of continuous Petri nets with variable speed (VCPN). A model of VCPN is suggested for the analysis and control design in urban and interurban networks. The proposed model provides representation for both motorway corridors and complex road junctions.

Firing and enabling sequences estimation for timed Petri nets

Petri nets (PNs) are useful tools for the modeling and analysis of discrete event systems. This work deals with the estimation of firing and enabling sequences for timed transition PNs with unknown time delays. The marking and reserved marking of the places are measured online. The estimation problem has exact and approximated solutions that are described. Sufficient conditions are given on the measurement accuracy of the marking and reserved marking vectors, so that the estimation of firing and enabling sequences is an exact one. If the estimation provides several solutions, the PN is extended in order to give a unique solution. Numerical aspects of the estimation are also investigated. As a consequence of this, the proposed method provides interesting tools for the modeling, performance analysis, and above all the monitoring of manufacturing systems and road traffic networks.

Fuzzy control of variable speed continuous Petri nets

Fuzzy logic theory is used to model and control a particular class of Petri nets called variable speed continuous Petri nets (VCPNs). In particular, we realize a fuzzy multimodeling of each transition of the VCPN. Each fuzzy rule is linear. The main advantage of the proposed method is that we provide after defuzzification the exact modeling of variable speed continuous Petri nets. Then a control strategy is elaborated and applied to VCPNs. Using this fuzzy multimodel, we develop a fuzzy control for variable speed continuous Petri nets and give efficient results on convergence for the global system. Upper and lower bounds of the convergence are presented. Finally, an example is worked out for the fuzzy control of VCPNs by the mean of a proportional control law.

Fuzzy multimodel of timed Petri nets

This paper deals with discrete event systems (DES) modeled either by discrete timed Petri nets without conflict or by continuous Petri nets. A fuzzy rule-based multimodel is developed for this kind of system. The behavior of each Petri net transition is described by the combination of two linear local fuzzy models. Using the Takagi-Sugemo model in a systematic way, we define the exact modeling for both classes of timed Petri nets. As a result, we notice that classical sets result in the exact description of discrete timed Petri nets. On the contrary, only fuzzy sets are suitable to describe continuous Petri nets exactly. The proposed fuzzy multimodels are very interesting from a control point of view. In that sense, general results such as convergence for timed Petri nets are given.

On analysis of discrete singularly perturbed non-linear systems: Application to the study of stability properties

Abstract Recently we have introduced a model of singular perturbation for discrete-time non-linear systems. This paper is aimed at validating the proposed model. In fact, a discrete version of the well-known Tikhonovs theorem on singular perturbation of continuous-time systems is established. The second aim is to study stability problems of such systems. Sufficient conditions for both asymptotic and exponential stability are obtained. As a result, significant order reduction of stability problems is achieved. This is achieved by allowing a small parameter whose upper bound is estimated. Finally a simple example is given to illustrate the applications of the results.

Optimal control of a particular class of singularly perturbed nonlinear discrete-time systems

This note studies a class of discrete-time nonlinear systems which depend on a small parameter. Using the singular perturbation theory in a systematic way, we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models. This decomposition is used to analyze optimal control via maximum principle of such systems. As a result, significant order reduction of optimal control problems is achieved.

Stabilization and regulation of class of non-linear singularly perturbed discrete-time systems

Abstract A class of discrete-time nonlinear systems which are two-time-scale is treated. Using the singular perturbation theory in a systematic way, we present a mode-decoupling approach which yields two separate subsystems containing the slow and fast parts. Furthermore, a two-time-scale analysis and design procedure for stabilization and regulation is presented. The controllability and stabilizability invariance of the fast subsystem is shown and an asymptotic stabilizing composite feedback control is proposed. Finally, it is shown that the composite control produces a finite cost which tends to the optimal cost of a slow problem as the singular perturbation parameter tends to zero.

Neural networks implementation for modeling and control design of manufacturing systems

This paper presents a dynamic neural network implementation for the modeling and control design of a class of manufacturing systems. The evolution of the considered systems is supposed to be continuous and non-stochastic. A separate implementation of the system elements is detailed. These elements are then connected together in order to obtain a global net that simulates the behavior of the real system. The obtained model is modular and can be adapted easily for any modification of the system. Permanent correction rules are developed to control the speed of the machines according to a desired profile and to take into consideration the buffers limited capacities. The convergence of the control design is proved. The proposed approach is applied on an exhaust valves assembly workshop.

A (max, plus) modelling approach for the evaluation of travelling times in a public transportation system

Extends the simplet transportation network model proposed in Nait-Sidi-Moh et al. (2002). We are interested in a public transportation system composed of several lines and several connection stops. The performance analysis and the evaluation of the travelling times at the connection stops are the main objectives of this study. Then to reach these goals we use a subclass of Petri nets to model our transportation network. By taking into account the network working, some structural conflicts appear in the graphical model. Then we solve them by determining routing equations. We represent our model by a non-stationary linear ( max, plus) system in the (max, plus) algebra. The resolution of this state model enables us to evaluate the system performances. Finally a numerical example is presented to illustrate the proposed model.

REDUCED ORDER MODELLING OF TWO-TIME-SCALE DISCRETE NON-LINEAR SYSTEMS

Abstract Application of two-time scale discrete singular perturbation methods have been limited to the linear systems. The area of discrete-time non-linear systems has received little attention. This paper deals with the singular perturbation model of non-linear discrete-time dynamic systems. We present a specific modelling and a mode decoupling approach well adapted for such systems. A comparison principle is used for grouping slow and fast states of a class of non-linear discrete systems. Finally, an example is given to show the feasibility of the theoretical results.