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This paper addresses the topic of output feedback stabilization of general one-dimensional reaction–diffusion partial differential equations (PDEs) in the presence of a saturation in the measurement. The boundary control and the second boundary condition take the form of Dirichlet/Neumann/Robin boundary conditions. The measurement is selected as a boundary Dirichlet trace. The boundary measurement, as available for feedback control, is assumed to be subject to a saturation. In this context, we achieve the local exponential stabilization of the reaction–diffusion PDE while estimating a subset of the domain of attraction of the origin.

The boundary feedback control of networks of freeway traffic is considered in this article by means of the partial differential equation (PDE)-based techniques. The control and measurements are all located at the boundaries of each link. We have established the boundary control model for the system, a linear hyperbolic system of balance laws, which includes not only the traffic flow dynamics of the network described by combining the linearized Aw-Rascle-Zhang (ARZ) traffic flow model of each link but also the integrated on-ramping metering and variable speed limit control modeled as the boundary condition. As the traffic demand of the network is fluctuated, the boundary input-to-state stability (ISS) controller is designed to suppress the disturbance and regulate the traffic flow into the boundedness regions of the desired states. Based on a novel Lyapunov function, some sufficient conditions in terms of the matrix inequalities are derived for the ISS boundary stabilization in the L²-norm. The numerical simulation is given to illustrate the effectiveness of the developed boundary feedback control. Moreover, an interesting traffic experiment is carried out by using the traffic simulation software, AIMSUN, and some specific traffic data are collected and analyzed to verify the feasibility and effectiveness of the boundary control.

International audience; In this paper the problem of set-point regulation of linear operator semigroups is considered, in presence of saturation of the control input. It is shown how global exponential stability can still be obtained by adding an anti-windup loop to the integral action. As first contribution towards the solution of this regulation problem, we give some new results related to the characterization of global exponential stability of the equilibrium of a subclass of semi-linear dynamical systems.

International audience; In this work we deal with the exponential stability of the nonlinear Kortewegde Vries (KdV) equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then we state an exponential stabilization result using a Lyapunov function by imposing small initial data and a restriction over the lengths. In this part also, we are able to obtain an explicit expression for the rate of decay. Then we prove the exponential stability of the solutions without restriction on the lengths and for small initial data, this result is based on an observability inequality. After that, we obtain a semi-global stabilization result working directly with the nonlinear system. Next we study the case where it may happen that a control domain with delay is outside of the control domain without delay. In that case, we obtain also a local exponential stabilization result. Finally, we present some numerical simulations in order to illustrate the stabilization.

International audience; In this work, we deal with the global well-posedness and stability of the linear and nonlinear Korteweg-de Vries equations on a finite star-shaped network by acting with saturated controls. We obtain the global well-posedness by using the Kato smoothing property for the linear case and then using some estimates and a fixed point argument we deal with the nonlinear system. Finally, we obtain the exponential stability using two different kinds of saturation by proving an observability inequality via a contradiction argument.

This thesis aims at identifying theoretically and concretely how visual analytics can support historians in their social network analysis process. Historical social network analysis is a method to study social relationships between groups of actors (families, institutions, companies, etc.) through a reconstruction of relationships of the past from historical documents, such as marriage acts, migration forms, birth certificates, and censuses. The use of visualization and analytical methods lets social historians explore and describe the social structure shaping those groups while explaining sociological phenomena and individual behaviors through computed network measures. However, the inspection and encoding of the sources leading to a finalized network is intricate and often results in inconsistencies, errors, distortions, and traceability problems, and current visualization tools typically have usability and interpretability issues. For these reasons, social historians are not always able to make thorough historical conclusions: many studies consist of qualitative descriptions of network drawings highlighting the presence of motifs such as cliques, components, bridges, etc. The goal of this thesis is therefore to propose visual analytics tools integrated into the global social historians' workflow, with guided and easy-to-use analysis capabilities. From collaborations with historians, I formalize the workflow of historical network analysis starting at the acquisition of sources to the final visual analysis. By highlighting recurring pitfalls, I point out that tools supporting this process should satisfy traceability, simplicity, and document reality principles to ease bask and forth between the different steps, provide tools easy to manipulate, and not distort the content of sources with modifications and simplifications. To satisfy those properties, I propose to model historical sources into bipartite multivariate dynamic social networks with roles as they provide a good tradeoff of simplicity and expressiveness while modeling explicitly the documents, hence letting users encode, correct, and analyze their data with the same abstraction and tools. I then propose two interactive visual interfaces to manipulate, explore, and analyze this data model, with a focus on usability and interpretability. The first system ComBiNet allows an interactive exploration leveraging the structure, time, localization, and attributes of the data model with the help of coordinated views and a visual query system allowing users to isolate interesting groups and individuals, and compare their position, structures, and properties. It also lets them highlight erroneous and inconsistent annotations directly in the interface. The second system, PK-Clustering, is a concrete proposition to enhance the usability and effectiveness of clustering mechanisms in social network visual analytics systems. It consists in a mixed-initiative clustering interface that let social scientists create meaningful clusters with the help of their prior knowledge, algorithmic consensus, and interactive exploration of the network. Both systems have been designed with continuous feedback from social historians, and aim to increase the traceability, simplicity, and document reality of visual analytics supported historical social network research. I conclude with discussions on the potential merging of both tools, and more globally on research directions towards better integration of visual analytics systems on the whole workflow of social historians. Systems with a focus on those properties---traceability, simplicity, and document reality---can limit the introduction of bias while lowering the requirements for the use of quantitative methods for historians and social scientists which has always been a controversial discussion among practitioners.; Cette thèse vise à identifier théoriquement et concrètement comment l'analyse visuelle peut aider les historiens dans leur processus d'analyse de réseaux sociaux. L'analyse de réseaux sociaux est une méthode utilisée en histoire sociale qui vise à étudier les relations sociales au sein de groupes d'acteurs (familles, institutions, entreprises, etc.) en reconstruisant les relations du passé à partir de documents historiques, tels que des actes de mariages, des actes de naissances, ou des recensements. L'utilisation de méthodes visuelles et analytiques leurs permet d'explorer la structure sociale formant ces groupes et de relier des mesures structurelles à des hypothèses sociologiques et des comportements individuels. Cependant, l'inspection, l'encodage et la modélisation des sources menant à un réseau finalisé donnent souvent lieu à des erreurs, des distorsions et des problèmes de traçabilité, et les systèmes de visualisation actuels présentent souvent des défauts d'utilisabilité et d'interprétabilité. En conséquence, les historiens ne sont pas toujours en mesure de faire des conclusions approfondies à partir de ces systèmes : beaucoup d'études se limitent à une description qualitative d'images de réseaux, surlignant la présence de motifs d'intérêts (cliques, îlots, ponts, etc.). Le but de cette thèse est donc de proposer des outils d'analyse visuelle adaptés aux historiens afin de leur permettre une meilleur intégration de leur processus global et des capacités d'analyse guidées. En collaboration avec des historiens, je formalise le processus d'une analyse de réseau historique, de l'acquisition des sources jusqu'à l'analyse finale, en posant comme critère que les outils utilisés dans ce processus devraient satisfaire des principes de traçabilité, de simplicité et de réalité documentaire (i.e., que les données présentées doivent être conformes aux sources) pour faciliter les va-et-vient entre les différentes étapes et la prise en main par l'utilisateur et ne pas distordre le contenu des sources. Pour satisfaire ces propriétés, je propose de modéliser les sources historiques en réseaux sociaux bipartis multivariés dynamiques avec rôles. Ce modèle intègre explicitement les documents historiques sous forme de nœuds, ce qui permet aux utilisateurs d'encoder, de corriger et d'analyser leurs données avec les mêmes outils. Je propose ensuite deux interfaces d'analyse visuelle permettant, avec une bonne utilisabilité et interprétabilité, de manipuler, d'explorer et d'analyser ce modèle de données. Le premier système ComBiNet offre une exploration visuelle de l'ensemble des dimensions du réseau à l'aide de vues coordonnées et d'un système de requêtes visuelles permettant d'isoler des individus ou des groupes et de comparer leurs structures topologiques et leurs propriétés. L'outil permet également de détecter les motifs inhabituels et ainsi de déceler les éventuelles erreurs dans les annotations. Le second système, PK-Clustering, est une proposition d'amélioration de l'utilisabilité et de l'efficacité des mécanismes de clustering dans les systèmes de visualisation de réseaux sociaux. L'interface permet de créer des regroupements pertinents à partir des connaissances a priori de l'utilisateur, du consensus algorithmique et de l'exploration du réseau dans un cadre d'initiative mixte. Les deux systèmes ont été conçus à partir des besoins et retours continus d'historiens, et visent à augmenter la traçabilité, la simplicité, et la réalité documentaire des sources dans le processus d'analyse de réseaux historiques. Je conclus sur la nécessité d'une meilleure intégration des systèmes d'analyse visuelle dans le processus de recherche des historiens. Cette intégration nécessite des outils plaçant les utilisateurs au centre du processus avec un accent sur la flexibilité et l'utilisabilité, limitant ainsi l'introduction de biais et les barrières d'utilisation des méthodes quantitatives, qui subsistent en histoire.