Papers by Laurent Hardouin
HAL (Le Centre pour la Communication Scientifique Directe), 2016
Max-plus linear systems are often used to model transportation networks, communications systems a... more Max-plus linear systems are often used to model transportation networks, communications systems and manufacturing systems. One way of controlling this kind of systems consists in choosing the date of input events in order to achieve the desired performances, e.g., to obtain output events in order to respect given dates. This kind of control is optimal, according to a just-in-time criterion, if the inputevent dates are delayed as much as possible while ensuring the output events to occur before a desired reference date. In this context, this paper presents an observed-based controller approach, where only a linear combination of the states, obtained from measurement, is available for the controller. As in the classical sense, this is a state-feedback control problem, which is solved in two steps: first an observer computes an estimation of the state by using the input and the output measurements, then this estimated state is used to compute the state-feedback control action. As a main result, it is shown that the optimal solution of this observer-based control problem leads to a greater control input than the one obtained with the output feedback strategy. A high throughput screening example in drug discovery illustrates this main result by showing that the scheduling obtained from the observer-based controller is better than the scheduling obtained from the output feedback controller.
Springer eBooks, 2009
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 13, 2019
IEEE Transactions on Automatic Control, Dec 1, 2003
This paper deals with the model-reference control of timed event graphs using the dioid algebra a... more This paper deals with the model-reference control of timed event graphs using the dioid algebra and the residuation theory. It proposes a control structure based on a precompensator and a feedback controller to improve the controlled system performance. It is shown that this approach always leads to an optimal behavior of the closed-loop system. An example is given to illustrate the proposed approach.
Interval analysis in diod : Application to robust controller design for Timed Event Graphs
HAL (Le Centre pour la Communication Scientifique Directe), 2004
2022 European Control Conference (ECC), Jul 12, 2022
This paper presents a mathematical tool for stochastic filter design based on reach sets for gene... more 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 approaches in have exponential complexity, which is an important drawback in higher-dimensional systems. In this work, we propose a max-plus polyhedra-based procedure with complexity that is in practice polynomially-bounded.
This paper deals with the model-reference control of max-plus linear systems. The main contributi... more This paper deals with the model-reference control of max-plus linear systems. The main contribution of this work is a general control structure that encompasses the previous one found in the literature. It is based on the RST-structure for conventional differentiable system. In addition it provides a comparison among some sub-structures and simulation results are presented.
AnIntegratedControlStrategytoSolvetheDisturbance DecouplingProblemforMax-PlusLinearSystemswith ApplicationstoaHighThroughputScreeningSystem ?
This paper presents the new investigations on the disturbance decoupling problem (DDP) for the ge... more This paper presents the new investigations on the disturbance decoupling problem (DDP) for the geometric control of maxplus 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 further delays on the output parts than the existing delays caused by the system breakdown. The new proposed modied disturbance decoupling problem (MDDP) in this paper ensures that the controlled output signals will not delayed more than the existing delays caused by the disturbances in order to achieve the just-in-time optimal control. Furthermore, this paper presents the integration of output feedback and open-loop control strategies to solve for the MDDP, as well as for the DDP. If these controls can only solve for the MDDP, but not for the DDP, an evaluation principal is established to compare the distance between two output signals generated by controls solving for the MDDP and DDP, respectively. This distance can be interpreted as the number of tokens or rings that are needed in order for the controls to solve for the DDP. Moreover, another alternative approach is nding a new disturbance mapping in order to guarantee the solvability of the DDP by the same optimal control for the MDDP. The main results of this paper are illustrated by using a timed event graph model of a high throughput screening system in drug discovery.
IFAC Proceedings Volumes, 2010
This paper deals with the observer design for max-plus linear systems. The approach is based on t... more 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.
HAL (Le Centre pour la Communication Scientifique Directe), 2011
HAL (Le Centre pour la Communication Scientifique Directe), Sep 18, 2011
This paper proposes a particle filter for linear max-plus systems. A brief introduction to discre... more This paper proposes a particle filter for linear max-plus systems. A brief introduction to discrete event systems is presented in a max-plus context. The paper describes some fundamental results in particle filtering and applies these results to the max-plus linear systems leading to a stochastic filtering algorithm. An example illustrates the method and some conclusions are drawn.
HAL (Le Centre pour la Communication Scientifique Directe), 2016
HAL (Le Centre pour la Communication Scientifique Directe), Dec 12, 2011
The control of timed Petri nets subject to synchronization and time delay phenomena is addressed ... more The control of timed Petri nets subject to synchronization and time delay phenomena is addressed in this paper. This class of timed Petri nets can be described by using the max-plus algebra. The objective is to design a feedback controller for a max-plus linear system to ensure that the system evolution respects time constraints imposed to the state that can be expressed by a semimodule. In order to achieve this goal, an approach based on the definition of the super-eigenvector of a matrix is proposed. Under some conditions, it ensures the existence of a feedback and allows us to compute it. The contribution is illustrated by a transportation control problem taken from literature.
Journal européen des systèmes automatisés, Nov 10, 2009
LeCorrconc]@univ-angers.fr RÉSUMÉ. Les Graphes d'Evénements Temporisés (GET) ordinaires admettent... more LeCorrconc]@univ-angers.fr RÉSUMÉ. Les Graphes d'Evénements 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 Z 2 . Ce papier tente une représentation graphique analogue pour les GET Généralisés, c'est-à-dire les GET dont les arcs sont valués. La représentation nécessite une dimension supplémentaire permettant de tenir compte du gain de ces systèmes qui est algébriquement modélisé par l'introduction de nouveaux opérateurs. Cette représentation est une extension naturelle de celle utilisée pour les GET ordinaires. Il est en outre montré que pour les GETG possédant une propriété de
Manufacturing systems are frequently adapted to changing customer demands. However, every extensi... more Manufacturing systems are frequently adapted to changing customer demands. However, every extension with respect to the hardware requires a modification of the corresponding model and controller. In this paper we propose a dioid model of manufacturing processes in which parts may visit the same resource more than once. The proposed model can be used to determine a controller that maintains the throughput while starting activities just-in-time. Furthermore, the model can easily be adapted in case of hardware modifications. Also nested processes, i.e., processes in which some activities of part k may be executed prior to activities of part (k -1), can be modeled with the proposed approach.
Lecture Notes in Control and Information Sciences, 2013
This chapter deals with the control of discrete-event systems which admit linear models in dioids... more This chapter deals with the control of discrete-event systems which admit linear models in dioids (or idempotent semirings), introduced in the previous chapter (see also the books ). These systems are characterized by synchronization and delay phenomena. Their modeling is focused on the evaluation of the occurrence dates of events. The outputs correspond to the occurrence dates of events produced by the system and the inputs are the occurrence dates of exogenous events acting on it. The control of the system inputs will lead to a scheduling of these occurrence dates such that a specified objective for the system be achieved. For example, in a manufacturing management context, the controller will have to schedule the input dates of raw materials or the starting of jobs in order to obtain required output dates for the produced parts.
Scheduling and control of high throughput screening systems with uncertainties and disturbances
Production and Manufacturing Research: An Open Access Journal, Jun 23, 2022
Timed Event Graphs (TEGs) and their weighted extension WTEGs are particular timed Discrete Event ... more 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 WTEG. Furthermore, we propose a control strategy which determines an optimal input for a predefined reference output. In this case, "optimal" means that input events are scheduled as late as possible with the restriction that the output events of the system do not occur later than specified by the reference. This strategy is often referred to as "just-in-time" control in literature.
The topic of this paper is the modeling and control of a class of timed Petri nets with resource ... more 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 residuation theory, an optimal control policy is developed, where optimality is in the sense of a lexicographical order reflecting the chosen prioritization of subsystems.
The topic of this paper is modeling and control of timed discrete event systems in a dioid framew... more The topic of this paper is modeling and control of timed discrete event systems in a dioid framework if systems operate under the restriction of shared resources. The behavior of such systems can be elegantly modeled using the Hadamard product of series in dioids. Using residuation of the Hadamard product, it is possible to compute optimal control, where optimality is in the sense of a lexicographical order reflecting the chosen prioritization of subsystems. The paper concludes with an example, illustrating the efficiency of the proposed method.
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Papers by Laurent Hardouin