Optimalsteuerung zeitbehafteter Synchronisationsgraphen mit Ressourcenkonkurrenz und Aktualisierung von Referenzsignalen

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 is not a TEG. We propose a formal method to determine the optimal control input for such systems, where optimality is in the sense of the widely adopted just-in-time criterion. Our approach is based on a prespecified priority policy for the TEG components of the overall system. It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework (idempotent semirings such as the max-plus or the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear time-invariant equations.Zeitbehaftete Synchronisationsgraphen (ZSGen) bilden eine spezielle Klasse zeitbehafteteter Petri-Netze. Sie können Synchronisations- und Verzögerungsphänomene modellieren, nicht aber Konflikte. Wir untersuchen ein Szenario, in dem sich mehrere ZSGen eine oder mehrere Ressourcen teilen und die Referenzsignale der ZSGen unvorhersehbaren Änderungen unterworfen sind. Da die beteiligten ZSGen um Ressourcen konkurrieren, ist das Gesamtsystem kein ZSG. Wir beschreiben eine formale Vorgehensweise zur Bestimmung des im just-in-time Sinne optimalen Stellsignals für dieses Gesamtsystem. Unser Ansatz basiert auf einer vorab festgelegten Priorisierung der einzelnen ZSGen. Er baut auf der existierenden Regelungstheorie für ZSGen auf und nutzt die Tatsache, dass sich die zeitliche Entwicklung von ZSGen in einem geeigneten mathematischen Rahmen (idempotente Halbringe wie beispielsweise die max-plus- oder die min-plus-Algebra) durch lineare zeitinvariante Gleichungen beschreiben lässt

Analysis of Periodic Discrete Event Systems in (Max,+) Algebra

International audienceDiscrete Event Dynamic Systems modeled by (max,+) linear equations with periodically varying coefficients are studied. It turns out that spectral properties of the so-called monodromy matrix can be used for the performance evaluation of these systems

An integrated control strategy to solve the disturbance decoupling problem for max-plus linear systems with applications to a high throughput screening system

International audienceThis 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 further delays on the output parts than the existing delays caused by the system breakdown. The new proposed modified disturbance decoupling problem (MDDP) in this paper ensures that the controlled output signals will not be 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 principle 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 firings that are needed in order for the controls to solve for the DDP. Moreover, another alternative approach is finding 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.</p

Analyse d'atteignabilité des systèmes (max,+)-linéaires à l'aide des polyèdres tropicaux

International audienc

The Hadamard product, its residual, and its dual residual in the dioid of counters: algorithms and implementation in C++

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++ implementation.Comment: 26 pages, 2 figures, technical repor

Estimation of Discrete-Event Systems using Interval Computation

International audienceDiscrete-event systems are driven by events and genrate events. To describe their evolution, the dater approach associate to each event a sequence of dates, namely a dater, corresponding to the dates at which the event occurs. In this paper, we show that for a large class of discrete-event systems, the dater approach makes it possible to cast the characterization of the set of all parameters that are consistent with some collected dater, in a bounded-error context, into a set-inversion framework. Set inversion consists of characterizing the reciprocal image of a given set by a known function. Provided that an inclusion function is known for the function to be inverted, the characterization can be performed by the interval-based algorithm SIVIA. A short presentation of this algorithm is recalled in this paper. The approach is illustrated through three examples

On Tropical Fractional Linear Programming

Abstract 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 solutions of tropical equations, a subject that was discussed in a previous work of the author

Genome-Wide Association Study in BRCA1 Mutation Carriers Identifies Novel Loci Associated with Breast and Ovarian Cancer Risk

BRCA1-associated breast and ovarian cancer risks can be modified by common genetic variants. To identify further cancer risk-modifying loci, we performed a multi-stage GWAS of 11,705 BRCA1 carriers (of whom 5,920 were diagnosed with breast and 1,839 were diagnosed with ovarian cancer), with a further replication in an additional sample of 2,646 BRCA1 carriers. We identified a novel breast cancer risk modifier locus at 1q32 for BRCA1 carriers (rs2290854, P = 2.7×10-8, HR = 1.14, 95% CI: 1.09-1.20). In addition, we identified two novel ovarian cancer risk modifier loci: 17q21.31 (rs17631303, P = 1.4×10-8, HR = 1.27, 95% CI: 1.17-1.38) and 4q32.3 (rs4691139, P = 3.4×10-8, HR = 1.20, 95% CI: 1.17-1.38). The 4q32.3 locus was not associated with ovarian cancer risk in the general population or BRCA2 carriers, suggesting a BRCA1-specific associat

Sur la commande linéaire de systèmes à événements discrets dans l'algèbre (max,+).

Ce mémoire a pour vocation de prouver aux membres du jury ma capacité à diriger des recherches. Il est organisé de la manière suivante : La première partie regroupe mon curriculum vitae, et une liste de publications. Le chapitre 2 est une présentation générale d'une partie des travaux que j'ai initié au cours de la dernière décennie. Dans un souci de cohérence d'ensemble je n'ai présenté que les travaux relatifs à la commande de systèmes (max,+) linéaires. Ils constituent le dénominateur commun aux trois thèses que j'ai encadrées. Ce chapitre inclut quelques nouveautés à l'attention du lecteur averti, notamment la synthèse d'un observateur d'état est introduite pour la première fois ici. Il se termine sur la présentation de quelques perspectives de recherche. La troisième partie regroupe quelques publications qui permettront au lecteur de retrouver les preuves des résultats énoncés dans le second chapitre