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Scalable large-scale control of network aggregates


Directeur de thèse :     Carlos CANUDAS-DE-WIT

Co-encadrant :     Paolo FRASCA

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Automatique Traitement du signal et des images

Structure de rattachement : CNRS

Établissement d'origine : Saint-Petersburg State University (Russie)

Financement(s) : Erc ; Sans financement


Date d'entrée en thèse : 01/09/2018

Date de soutenance : 02/09/2021


Composition du jury :
WITRANT Emmanuel, Professeur, Université Grenoble Alpes, Président du jury
DI BERNARDO Mario , Professeur, University of Naples Federico II, Rapporteur
BAMIEH Bassam , Professeur, University of California, Santa Barbara, Rapporteur
KRSTIC Miroslav , Professeur, University of California, San Diego, Examinateur
D'ANDREA-NOVEL Brigitte , Professeure, Institut de Recherche et de Coordination Acoustique/Musique, Examinatrice
EBELS Ursula , Professeure, CEA Grenoble, Invitée


Résumé :
This research is done in the context of European Research Council's (ERC) Advanced Grant project Scale-FreeBack. The aim of Scale-FreeBack project is to develop a holistic scale-free control approach to complex systems, and to set new foundations for a theory dealing with complex physical networks with arbitrary dimension. The contributions of the present PhD work are mainly related to the problems of modeling and control design for large-scale systems. We seek simplified model representations for control purposes for different classes of large-scale systems, from networks to PDEs. Within this PhD thesis, we propose control design techniques that completely rely on aggregated models of original large-scale systems.
First of all, we deal with large linear networks by controlling their average state and the deviation of all the states from the average. The problem of controlling the average state with integral controller is studied, and a simple relation between positivity of the system and its passivity is established. The deviation is then minimized via constrained extremum seeking method. This approach is generalized to control a general multidimensional linear output and simultaneously minimize a general scalar quadratic output.
Then, we turn our attention to the PDE systems and a simplified representation of their solutions. In particular, we develop a shape-based model reduction technique applicable to 1D conservation laws, which assumes a particular shape parametrization of the PDE's solutions and then transforms the PDE into a system of ODEs describing the evolution of these shape parameters.
Finally, we study the problem of deriving continuous representations of large-scale spatially-distributed systems. Namely, we develop a continuation method which transforms any general nonlinear system with spatial structure into a PDE model. We further provide an analysis of accuracy and convergence of such representation in the linear case. The method is useful since it opens new possibilities for analysis and control design in continuous domain for intrinsically discrete systems.
In the thesis we elaborate various applications of the continuation method. In particular, we apply the method to several problems of transportation networks and multi-agent systems, providing derivations of continuous models for traffic systems, an original solution to the Hilbert's 6th problem of the derivation of Euler equations from Newtonian systems of particles, and a control design technique for a large robotic formation on a density level. Finally we apply the method to the large-scale networks of oscillators (such as lasers or spin-torque oscillators). The obtained PDE models are used for control purposes (such as boundary stabilization via PDE-based backstepping) and for the analysis, deriving conditions for the existence and stability of synchronous solutions in systems with both homogeneous and inhomogeneous oscillators.

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