Our hyperconnected world is built on systems such as the Internet, the global banking system, the power grid, 5G and the Internet of Things. However, this growing entanglement is accompanied by an increased requirement to understand and control the complex dynamics that can emerge from these interconnections. However, it seems unrealistic to envisage centralized control solutions for these complex systems, in which a node would have all the information on the network and could control it globally. Our work therefore concerns the design of decentralized and distributed control laws, where the controllers communicate locally rather than globally. Such control strategies are better suited to the current reality: they tend to be more efficient in terms of communication requirements, fault diagnosis, and maintenance. The design of such control structures and algorithms is however ambitious, because they must collectively meet global objectives while acting locally. The time-delays, another source of complexity, inevitably appear in these situations. Such delays are inherent in the communication network, but also in the calculation latencies occurring at the level of the sensors and actuators (which must often save their energy). Until now, the methods available for the design of decentralized or distributed controllers have not been easily applicable to systems with multiple delays. Furthermore, the underlying theoretical framework was not suitable for complex systems where the overall dynamics are largely determined by the interactions of the individual components. In this thesis, a general approach is presented to design distributed and decentralized controllers for systems with delays. Furthermore, a scalable and computationally efficient algorithm for the design of distributed control is presented for a class of large-scale interconnected systems. It uses a graph theoretic approach and is suitable for subsystems with identical models. In addition, we extend the results to consider heterogeneity in subsystems. We propose an approach for the design of robust decentralized controllers, which are robust with respect to model uncertainties and communication imperfections (such as time-varying delays, aperiodic sampling , asynchronism, and noise).
Directeur de thèse : Jean-Pierre RICHARD, Professeur, Centrale Lille Institut, V. d’Ascq Co-Directeurs de thèse : Wim MICHIELS, Professeur, KU Leuven, Belgique Rapporteurs : Constantin MORARESCU, Professeur, Université de Loraine, CRAN Luca ZACCARIAN, Directeur de Recherche CNRS, HDR, LAAS Toulouse Membres : Laurentiu HETEL, Chargé de Recherche CNRS, HDR, CRIStAL, V. d’Ascq Catherine BONNET, DR Inria, HDR, Inria Saclay Ile de France et L2S Centrale Supelec Maria Domenica DI BENEDETTO, Professeur, University of l'Aquila, Italie Goele PIPELEERS, Professeur KU Leuven & R&D Materialise, Belgique Stefan VANDEWALLE, Professeur, KU Leuven, Belgique Invités : Jean-Pierre RICHARD, Professeur, Centrale Lille Institut, V. d’Ascq