Laurent Hardouin

Laurent Hardouin
University of Angers | UA · Laboratoire Angevin de Recherche en Ingénierie des Systèmes

Professor University of Angers

About

234
Publications
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2,217
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January 1993 - August 2020
University of Angers
Position
  • Professor (Full)

Publications

Publications (234)
Article
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...
Article
The paper focuses on the set-estimation for uncertain Max-Plus Linear systems, with bounded random parameters. This estimation process involves determining the conditional reach set, which is a compact set of all possible states that can be reached from a previous set through the transition model (dynamics) and can lead to the observed measurements...
Article
Full-text available
This paper studies a scenario in which the occurrence of one or more events in a discrete event system is subject to external restrictions which may change unexpectedly during run-time. The system is modeled as a timed event graph (TEG) and, in this context, the presence of the aforementioned external restrictions has become known as partial synchr...
Conference Paper
Full-text available
This study compares an existing method with a novel approach for state estimation of Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering does not apply to this system class, despite computable posterior probability density function (PDF) support. Existing literature suggests a limited scalability disjunctive approac...
Article
This paper deals with the input-output representation of a class of timed Discrete Event Systems. The systems considered are those that can be described using Timed Event Graphs extended with weights on the arcs and clock rate modifiers or time varying delays. The model relies on periodic expressions using six elementary operators: shift, multiplic...
Conference Paper
Full-text available
A wide range of Discrete Event Systems (DES) such as manufacturing systems, telecommunications networks, transportation networks, and parallel computing, etc., can be modelled as max-plus systems in which maximization and addition are the main operations. In this paper, we use a nonlinear approach to deal with the error-estimation of nondeterminist...
Article
It is a well-known fact that the dynamics of timed event graphs (TEGs), a subclass of timed Petri nets able to model delay and synchronization phenomena, admits linear representation in dioids of formal power series. In order to model and control systems of TEGs with resource sharing phenomena, it is useful to extend the standard set of dioid opera...
Article
Full-text available
This paper presents a new approach to bounded error state-estimation for uncertain max-plus linear systems. This method yields the smallest interval vector including the real state in a guaranteed way. The parameters of the max-plus linear systems are assumed to be bounded, the nondeterministic measurement of the system output is assumed to be give...
Article
Full-text available
Timed event graphs (TEGs) are a subclass of timed Petri nets whose dynamics is governed by standard synchronization, i. e., a transition is enabled to fire a certain time after the firing of some other transition(s) and is never disabled by the firing of other transitions. Partial synchronization (PS) imposes an additional condition: a partially sy...
Article
Timed event graphs (TEGs) constitute a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. In a suitable mathematical framework (idempotent semirings such as the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear equations. Recently, a method has been proposed f...
Presentation
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These slides were used to present the paper "Implementation of procedures for optimal control of timed event graphs with resource sharing" (DOI: 10.1016/j.ifacol.2022.10.346) at the 16th IFAC Workshop on Discrete Event Systems (WODES 2022).
Article
This article aims to improve the stochastic filtering algorithm with bounded disturbances, proposed in 1. This filter is efficient for max-plus linear systems in explicit form, i.e., the timed event graph (TEG) described by this system is initially with one token on each place. Nevertheless, it needs strong assumptions in order to be accurate for s...
Conference Paper
Full-text available
This paper presents a mathematical tool for stochastic filter design based on reach sets for general Uncertain Max-Plus Linear (uMPL) systems. The reach sets are defined as the computation of the set of all states that can be reached from a known previous state vector (forward) and from an available source of measurement (backward). The existing ap...
Article
Full-text available
Based on the existing research work on the modeling and control of cyclically operated high-throughput screening systems, this paper presents the scheduling and control of high-throughput screening systems with uncertainties and disturbances. Different definitions of disturbance decoupling problems are considered in order to achieve the optimal sch...
Technical Report
Full-text available
This report presents the algorithms for computing the Hadamard product, its residual, and its dual residual between formal power series in the dioid of counters (which is isomorphic to M_in^ax[[γ, δ]]). The algorithms have been implemented in the C++ toolbox ETVO ((Event|Time)-Variant Operators), which, in turn, is based on the toolbox MinMaxgd. In...
Preprint
Full-text available
This report presents the algorithms for computing the Hadamard product, its residual, and its dual residual between formal power series in the dioid of counters. The algorithms have been implemented in the C++ toolbox ETVO ((Event|Time)-Variant Operators). After proving the correctness of the algorithms, we present a user guide for the C++ implemen...
Conference Paper
Full-text available
Le filtrage stochastique des systèmes max-plus linéaires incertains peut être réalisé grâce à l'algorithme proposé dans [21]. Dans la pratique, les systèmes max-plus linéaires incertains mettent en jeu des dépendances entre les états du système. Cette dépendance dégrade la qualité du filtrage proposé dans [21]à cause de la violation de l'hypothèse...
Article
Full-text available
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...
Conference Paper
Full-text available
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).
Conference Paper
Full-text available
Discrete-event systems exhibiting synchronization and delay phenomena can be modeled as timed event graphs (TEGs), which admit a linear representation in some idempotent semirings. For such linear systems, a control theory has been constructed. In this paper, we build onto this control framework by proposing a formal method to determine the optimal...
Article
Full-text available
Article
Full-text available
Timed event graphs (TEGs) are a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. We consider a scenario where a number of TEGs share one or several resources and are subject to changes in their output-reference signals. Because of resource sharing, the resulting overall discrete event system i...
Article
Full-text available
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...
Article
Full-text available
Max Plus Linear (MPL) systems are often described by a transition function, which models the state evolution of the system, and a measurement function, which binds the measures with the system states. Methods for computing the inverse image of a point w.r.t. the measurement function are particularly interesting in applications where it is desirable...
Article
Discrete-event systems exhibiting synchronization and delay phenomena, but not conflict, can be modeled as timed event graphs (TEGs), which admit a linear representation in some idempotent semirings. For such linear systems, a control theory has been constructed. In this paper, we build onto this control framework by proposing a formal method to de...
Article
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).
Article
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...
Conference Paper
Full-text available
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...
Poster
Full-text available
Les SystèmesSystèmes`Systèmesà Evénements Discrets (SED) peuventêtrepeuventêtre définis comme des systèmes dans lesquels les variables d'´ etat changent sous l'occurrence d'´ evènements au fil du temps. Les SED mettant en jeu des phénomènes de synchronisation peuventêtrepeuventêtre modélisés par deséquations deséquations linéaires dans les algèbres...
Technical Report
Full-text available
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.
Conference Paper
Full-text available
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...
Article
Full-text available
p>In this paper, we are interested in the general problem of estimating a linear function of the states for a given Max-Plus linear dynamical system. More precisely, using only the current and past inputs/outputs of the system, we want to construct a sequence that converges in a finite number of steps to the value given by a linear function of the...
Article
Full-text available
The objective of this work is to propose a filtering strategy for max-plus linear systems with bounded disturbances without the direct calculation of the a posteriori state probability. The strategy is based on the inversion of the expectation of the measure with respect to the state variable. Among the possible solutions, the closest to the predic...
Article
The reachability analysis problem of Max Plus Linear (MPL) systems has been properly solved using the Difference-Bound Matrices approach. In this work, the same approach is considered in order to solve the reachability analysis problem of MPL systems subjected to bounded noise, disturbances and/or modeling errors, called uncertain MPL (uMPL) system...
Article
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...
Article
Full-text available
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...
Book
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,...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Chapter
Full-text available
In this chapter, the dynamics of manufacturing systems is characterized through the occurrence of events such as parts entering or leaving machines. Furthermore, we assume that the relations between events are expressed by synchronizations (i.e., conditions of the form: for all k ≥ l, occurrence k of event e2 is at least τ units of time after occur...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Article
A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “Max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus r...
Book
Full-text available
p>In this chapter, the dynamics of manufacturing systems is characterized through the occurrence of events such as parts entering or leaving machines. Furthermore, we assume that the relations between events are expressed by synchronizations (i.e., conditions of the form: for all k ≥ l, occurrence k of event e2 is at least τ units of time after occ...
Article
This paper describes a robust model-based fault diagnosis approach that enables to enhance the sensitivity analysis of the residuals. A residual is a fault indicator generated from an analytical redundancy relation which is derived from the structural and causal properties of the signed bond graph model. The proposed approach is implemented in two...
Article
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...
Article
Full-text available
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...
Article
Two algorithms for solving a specific class of steady-state control problems for Timed Event Graphs are presented. In the first, asymptotic convergence to the desired set is guaranteed. The second algorithm, which builds on from the recent developments in the spectral theory of min-max functions, guarantees Lyapunov stability since the distance bet...
Conference Paper
Full-text available
The topic of this paper is the modeling and control of a class of timed Petri nets with resource sharing problems in a dioid framework. We first introduce a signal which denotes the number of resources available for each competing subsystem at each instant of time. Based on this signal, the overall system is modeled in min-plus algebra. Using resid...
Conference Paper
This paper presents robust controllers solving the disturbance decoupling problem(DDP) of a class of uncertain max-plus linear systems, whose system matrices vary between intervals with known lower and upper bounds. The DDP for such uncertain max-plus linear systems is defined as finding a control interval such that the output trajectory interval f...
Article
This paper presents the new investigations on the disturbance decoupling problem (DDP) for the geometric control of max-plus linear systems. The classical DDP concept in the geometric control theory means that the controlled outputs will not be changed by any disturbances. In practical manufacturing systems, solving for the DDP would require furthe...
Conference Paper
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...
Article
Full-text available
Two algorithms for solving a specific class of steady-state control problems for Timed Event Graphs are presented. In the first, asymptotic convergence to the desired set is guaranteed. The second algorithm, which builds on from the recent developments in the spectral theory of min-max functions, guarantees Lyapunov stability since the distance bet...
Conference Paper
This paper presents a sufficient condition to solve the observation problem in tropical linear event-invariant dynamical systems, where a linear functional of the states can be observed in a finite number of steps using only the information from inputs and outputs. Using the residuation theory, this solvability condition can be easily implemented i...
Conference Paper
Full-text available
This paper presents an integrated control strategy solving disturbance decoupling of max-plus linear systems. The classical disturbance decoupling problem (DDP) in geometric control theory means that the controlled outputs will not be changed by any disturbances. The new proposed modified disturbance decoupling problem (MDDP) ensures that the contr...
Article
Very recently, tropical counterparts of fractional linear programs have been studied. Some algorithms were proposed for solving them, with techniques ranging from bisection methods to homeomorphisms to formal power series. In this paper, some algorithms are also proposed. They mainly rely in the ability of finding the greatest and smallest solution...
Article
Full-text available
This paper presents a set membership method (named Interval Analysis Localization (IAL)) to deal with the global localization problem of mobile robots. By using a LIDAR (LIght Detection And Ranging) range sensor, the odometry and a discrete map of an indoor environment, a robot has to determine its pose (position and orientation) in the map without...
Article
Full-text available
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...
Article
Full-text available
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...
Article
An extension to an algorithm of R.A. Cuninghame-Green and K. Zimmermann for solving equations with residuated functions is presented. This extension relies on the concept of weak residuation and in the so-called “strong property”. It is shown that a contextualization of this method to tropical linear equations, which will be denoted as Primal Metho...
Chapter
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A small manufacturing process is considered, where two (different) parts A and B are pre-processed on two individual resources RAand RB. Once the pre-processing is done, a third resource RCassembles both parts to a final part C. Thus, resource RChas to wait for resource RAand RBto finish their processing, that is, the release of part A and the rele...