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Le Havre, France

The University of Le Havre is a French university, in the Academy of Rouen. Wikipedia.

Lefebvre D.,University of Le Havre
Nonlinear Analysis: Hybrid Systems | Year: 2011

Reliability analysis is often based on stochastic discrete event models like stochastic Petri nets (SPNs). For large dynamical systems with numerous components, the analytical expression of the SPNs steady state is full of complexities because of the combinatory explosion with discrete models. Moreover, the estimation of mean markings thanks to simulations is time consuming in case of rare events. For these reasons, Petri net fluidification may be an interesting alternative to provide a reasonable estimate of the asymptotic behavior of stochastic processes. Unfortunately, the steady states of SPNs and timed continuous Petri nets (contPNs) with the same structure, same initial marking and same firing rates are mainly often different. The region of SPN steady states (when firing rates are defined in a polyhedral area) contrasts with that of contPN ones. The purpose of this paper is to illuminate this issue in taking advantage of the piecewise-affine hybrid structure of contPNs. Regions and critical regions are defined in the marking space in order to characterize this structure. Based on this characterization, the main contribution is to propose a transformation of the considered SPN into a contPN with the same structure, modified firing rates and homothetic initial marking so that the corrected contPN converges partially to the same mean marking than the SPN. Consequently, a global understanding of an SPN steady state can be obtained according to the corrected contPN. © 2011 Elsevier Ltd.

Michel S.,University of Le Havre | Vanderbeck F.,University of Bordeaux 1
Operations Research | Year: 2012

Inventory routing problems combine the optimization of product deliveries (or pickups) with inventory control at customer sites. The application that motivates this paper concerns the planning of single-product pickups over time; each site accumulates stock at a deterministic rate; the stock is emptied on each visit. At the tactical planning stage considered here, the objective is to minimize a surrogate measure of routing cost while achieving some form of regional clustering by partitioning the sites between the vehicles. The fleet size is given but can potentially be reduced. Planning consists of assigning customers to vehicles in each time period, but the routing, i.e., the actual sequence in which vehicles visit customers, is considered an "operational" decision. The planning is due to be repeated over the time horizon with constrained periodicity. We develop a truncated branch-and-price-and-cut algorithm combined with rounding and local search heuristics that yield both primal solutions and dual bounds. On a large-scale industrial test problem (with close to 6,000 customer visits to schedule), we obtain a solution within 6.25% deviation from the optimal to our model. A rough comparison between an operational routing resulting from our tactical solution and the industrial practice shows a 10% decrease in the number of vehicles as well as in the travel distance. The key to the success of the approach is the use of a state-space relaxation technique in formulating the master program to avoid the symmetry in time. © 2012 INFORMS.

Odibat Z.M.,University of Le Havre
Nonlinear Dynamics | Year: 2010

This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have non-identical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to assess the performance of the proposed adaptive controller in synchronizing chaotic systems. © 2009 Springer Science+Business Media B.V.

Odibat Z.M.,University of Le Havre
Computers and Mathematics with Applications | Year: 2010

An analytic study on linear systems of fractional differential equations with constant coefficients is presented. We briefly describe the issues of existence, uniqueness and stability of the solutions for two classes of linear fractional differential systems. This paper deals with systems of differential equations of fractional order, where the orders are equal to real number or rational numbers between zero and one. Exact solutions for initial value problems of linear fractional differential systems are analytically derived. Existence and uniqueness results are proved for two classes. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approaches. © 2009 Elsevier Ltd. All rights reserved.

Lefebvre D.,University of Le Havre
Nonlinear Analysis: Hybrid Systems | Year: 2012

Reliability analysis is 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 investigated to estimate the asymptotic behavior of stochastic processes and the stationary indicators used for reliability issues. Unfortunately, the asymptotic mean markings of stochastic and continuous Petri nets are mainly often different. This paper proposes approximations of the stochastic steady state according to a set of reference data and to the classification of the firing rates, based on a k-nearest-neighbor method. This method maps the parameters of the stochastic model with the ones of the fluid model. It leads to the design of modified timed continuous Petri nets suitable to approximate the steady state of any stochastic Petri net. © 2012 Elsevier Ltd.

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