# Bertrand CottenceauUniversity of Angers | UA · ISTIA, école d'ingénieurs de l'Université d'Angers

Bertrand Cottenceau

PhD

## About

101

Publications

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Introduction

Additional affiliations

September 2013 - October 2014

September 2000 - August 2018

September 1996 - September 2013

## Publications

Publications (101)

Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1,t2 can only fire if both transiti...

This paper addresses observer design for Weighted Timed Event Graphs (WTEGs). WTEGs are a more general class of Timed Discrete Event Systems than standard Timed Event Graphs (TEGs). Hence our results represents a generalization of observer synthesis methods in Hardouin et al. (2007).

Timed Event Graphs (TEGs) can be described by time invariant (max,+) linear systems. This formalism has been studied for modelling, analysis and control synthesis for decision-free timed Discrete Event Systems (DESs), for instance specific manufacturing processes or transportation networks operating under a given logical schedule. However, many app...

This paper addresses observer design for Weighted Timed Event Graphs (WTEGs). WTEGs are a more general class of Timed Discrete Event Systems than standard Timed Event Graphs (TEGs). Hence our results represent a generalization of observer synthesis methods in Hardouin et al. (2007).

This paper deals with control of industrial systems which can be depicted by timed event graphs. A methodology and software tools are presented to allow engineers to implement automatically controllers in PLC. Three steps are needed and recalled: the modelling of the system in max plus algebra, the design of the controller and the implementation in...

Some classes of Discrete Event Systems can be studied using models in dioids, in particular by describing their dynamics using operators. Since the 1980s, this approach has enabled the study of Time Event Graphs (TEGs) through input-output models. The algebraic structure considered is then a set of formal series, denoted M ax in γ, δ , whose variab...

This report is an introduction to a C++ library to handle formal series for Discrete Event Systems. The ETVO library is able to handle some rational expressions with elementary operators necessary to describe Weighted Timed Event Graphs and Timed Event Graphs with Periodic holding times.

Certaines classes de Systèmes à Evénements Discrets (SED) peuvent être étudiées via des modèles sur des dioïdes, notamment en décrivant leur dynamique au moyen d'opérateurs. Le décalage temporel et le décalage dans la numérotation des événements sont dans ce cas assimilés à des opérateurs élémentaires. Depuis les années 80, cette approche a permis...

Contains the source files and the startup instructions to use ETVO in C++.

Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1, t2 can only fire if both transit...

Max-plus linear systems theory was inspired by and originated from classical linear systems theory more than three decades ago, with the purpose of dealing with nonlinear synchronization and delay phenomena in timed discrete event systems in a linear manner. Timed discrete event systems are driven by discrete events, are equipped with a notion of t...

Max-plus linear systems theory was inspired by and originated from classical linear systems theory more than three decades ago, with the purpose of dealing with nonlinear synchronization and delay phenomena in timed discrete event systems in a linear manner. Timed discrete event systems describe many problems in diverse areas such as manufacturing,...

Timed Event Graphs (TEGs) and their weighted extension WTEGs are particular timed Discrete Event Systems
(DESs) where the dynamic behavior is described by synchronization and saturation effects. With dioids, a linear systems theory has been developed for (weighted) TEGs. In this paper, we use dioid theory to model the input-output behavior of a WTE...

Timed event graphs (TEGs) are suitable to model manufacturing systems in which synchronization and delay phenomena appear. Since 1980s, TEGs are studied as a class of linear discrete event systems in idempotent semirings such as the (min,+) algebra. In this paper, we consider the class of weighted TEGs (WTEGs) that corresponds to TEGs where the edg...

For Timed Event Graphs (TEGs), model reference control is a well known approach to
stabilize and to improve the performance of a system. This method is based on dioid and residuation
theory. In this work, we study model reference control for the class of single-input and single-output
(SISO) Weight-Balanced Timed Event Graphs (WBTEGs), which is an...

For Timed Event Graphs (TEGs), model reference control is a well known approach to stabilize and to improve the performance of a system. This method is based on dioid and residuation theory. In this work, we study model reference control for the class of single-input and single-output (SISO) Weight-Balanced Timed Event Graphs (WBTEGs), which is an...

Max-plus algebra is a suitable algebraic setting to model discrete event systems involving synchronization and delay phenomena which are often found in transportation networks, communications systems, and manufacturing systems. One way of controlling this kind of systems consists in choosing the dates of input events in order to achieve the desired...

In this paper, we consider discrete event systems divided in a main system and a secondary system such that the innerdynamics of each system is ruled by standard synchronizations and the interactions between both systems are expressed bypartial synchronizations (i.e., event e2 can only occur when, not after, event e1 occurs) of events in the second...

We consider (max, +)-linear systems (i.e., discrete event systems ruled by conditions of the form: “for all k ≥l, occurrence k of event β2 is at least τ units of time after occurrence k-l of event e 1 ” with τ, l ∊ N 0 ) with the additional restriction that certain events can only occur at time instants in predefined ultimately periodic sets of int...

Communication (Communication avec actes dans un congrès)

Many methods exist to detect stable equilibrium points x∗x∗ of nonlinear dynamical systems ẋ=f(x). Most of them also prove the existence of a neighborhood NN of x∗x∗ such that all trajectories initialized in NN converge to x∗x∗. This paper provides a numerical method combining Lyapunov theory with interval analysis which makes to find a set NN whic...

The trade-off between energy consumption and execution time (i.e., for a given task, the faster it is achieved, the higher its energy consumption is) is investigated for systems modeled by timed event graphs. In this technical note, we aim to increase execution times (and, consequently, lower energy consumption) while preserving input-output and pe...

The class of timed event graphs (TEGs) has widely been studied thanks to an approach known as the theory of max-plus linear systems. In particular, the modeling of TEGs via formal power series in a dioid called MinMax[gamma ,delta] has led to input–output representations on which some model matching control problems have been solved. Our work attem...

Timed event graphs (TEGs) are a subclass of timed Petri nets suitable to model decision-free timed discrete event systems. In classical TEGs, exact synchronization of two transitions T1 and T2 is available by requiring that transitions T1 and T2 fire simultaneously. In this paper, a new sort of synchronization, namely partial synchronization, is in...

This paper deals with solution of inequality A ⊗ x {precedes above single-line equals sign} b, where A, x and b are interval matrices with entries defined over idempotent semiring. It deals also with the computation of a pair of intervals, (x, y) which satisfies the equation A ⊗ x = B ⊗ y. It will be shown that this equation may be solved by consid...

This paper deals with the state estimation for max-plus linear systems.
This estimation is carried out following the ideas of the observer
method for classical linear systems. The system matrices are assumed to
be known, and the observation of the input and of the output is used to
compute the estimated state. The observer design is based on the
re...

In this chapter, we will recall contributions to dioid theory dealing with control that were achieved during the last two decades. Just like in classical control engineering, control is to be understood as having an action on the inputs so as to adapt to given specifications. For instance, one could aim at finding an optimal control in order to tra...

The class of Timed Event Graphs (TEGs) has widely been studied for the last 30 years thanks to an algebraic approach known as the theory of Max-Plus linear systems. In par-ticular, the modeling of TEGs via formal power series has led to input-output descriptions for which some model matching control problems have been solved. The objective of this...

Based on the (min,+)-linear system theory, the work developed here takes the set membership approach as a starting point in order to obtain a container for ultimately pseudo-periodic functions representative of Discrete Event Dynamic Systems. Such a container, by approximating the exact system, ensures to entirely include it in a guaranteed way. To...

This paper deals with formal modelling of Petri nets including shared resources. These phenomena appear widely in the production management context, for the modelling of manufacturing cells. But, they usually cannot be formally represented in dioid algebraic structures based on sets of scalars. In this paper, we design a method to describe such a p...

According to the theory of Network Calculus based on the (min,+) algebra, analysis and measure of worst-case performance in
communication networks can be made easily. In this context, this paper deals with traffic regulation and performance guarantee
of a network i.e. with flow control. At first, assuming that a minimum service provided by a networ...

This paper deals with the observer design for max-plus linear systems. The approach is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring. An illustrative example allows to discuss about a practical implementation.

This technical note deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based...

According to the theory of Network Calculus based on the (min,+) algebra., analysis and measure of worst-case performance in communication networks can be made easily. In this context, this paper deals with traffic regulation and performance guarantee of a network i.e. with flow control. At first, assuming that a minimum service provided by a netwo...

This paper deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the re...

Les Graphes dtextquoterightEvénements Temporisés (GET) ordinaires admettent une relation de transfert linéaire dans les algèbres de type (min,+). Ces relations de transfert peuvent être décrites au moyen de séries ultimement périodiques représentables dans le plan 2. Ce papier tente une représentation graphique analogue pour les GET Généralisés, ct...

Based on the (min,+)-linear system theory, the work developed here takes the set approach as a starting point in order to obtain a container of functions representative of Discrete Event Systems. The latter is an interval whose upper bound is a convex function and lower bound is a concave function. In particular, it is shown that computations ' min...

This paper deals with the control of uncertain (min,+)-linear systems which belong to an interval. Thanks to the residuation
theory, a precompensator controller placed upstream of the studied system is given in such a way that even if the system’s
behavior is not perfectly known, it has the property to delay the input as much as possible while keep...

Routing is a prevailing aspect in job-shop systems. Each product is routed according to its own production cycle. However, routing phenomena, or equivalently conflicts in Petri nets, usually cannot be modelled in dioid algebraic structures such as ℤmin or ℤmax (also denoted (min,+) and (max,+). The main reason is that choices between several paths...

à Angers (France) les 17/03 et 18/03/2009

Résumé— Dans le cadre de la théorie des systèmes (max,+)-linéaires, ce document considère la transformée de Legendre-Fenchel afin d'obtenir une approximation convexe par valeur supérieure des séries périodiques représentatives de Systèmes à Événements Discrets. Les algorithmes per-mettant la manipulation de ces séries à travers une forme canonique...

This talk will present the Scilab toolbox for Network Calculus computation. It was developed thanks to the INRIA ARC COINC project (COmputational Issue in Network Calculus see http://perso.bretagne.ens-cachan.fr/~bouillar/coinc/spip.php?rubrique1). This software library deals with the computation of ultimate pseudo-periodic functions. They are very...

This paper deals with the control of uncertain (max,+)-linear systems, more precisely those of which parameters are not exactly known but assumed to belong to an interval. In this context, we aim at synthesizing a controller in order to reduce the uncertainty at the output of the controlled system. This study is possible thanks to the residuation t...

This paper deals with the disambiguation of the behaviour of Petri nets including shared resources. In the production management context, they are often used for the modelling of manufacturing cells. But this representation has a poor transposition into dioid algebra. In this article, we design a method to describe such a phenomenon in a dioid of i...

This article deals with a possible improvement of a Kanban policy due to a (max,+)-algebra analysis. We show that for a given Kanban system, it is possible to change the original feedback loop by a (max,+)-linear controller which keeps the same quality of service but reduces the work in process. This new control policy contains a (max,+)-linear dyn...

This paper deals with the computation of a maximal flow in single input single output (max, +) linear systems. Assuming known a system composed of some subsystems - each one being described by a transfer function and some secondary inputs interfering with the principal flow on consecutive sub-systems, the computation of a maximal principal output i...

This paper provides an eective method to create an abstract simplicial complex homotopy equivalent to a given set S described by non-linear inequalities (polynomial or not). To our knowledge, no other numerical algorithm is able to deal with this type of problem. The proposed approach divides S into subsets that have been proven to be contractible...

This paper presents a design method for a state observer of max-plus linear systems based on the observation of the input and the output, by assuming the knowledge of the system matrices. The observer design is done in an analogous way to the observer method for classical linear system. The paper will be concluded by an illustration.

This paper deals with a possible evolution of a Kanban system due to a (max,+)-algebra analysis. We show that for a given Kanban system, it is always possible to change the original Kanban policy by a (max,+)-linear policy which keeps the same quality of service but reduces the work in process. This new control policy contains a (max,+)-linear dyna...

CD-ROM à Angers (France) les 28 et 29/03/2006

In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connecte...