This thesis is a broad treatment of the distributed state estimation problem for linear systems. In this setting, a network of observer nodes collectively estimates the state of a dynamical system, since individually they are not able to do so. The proposed solution consists of a distributed observer which uses diffusive coupling and leads to three complementary contributions. The first one considers exponential convergence with arbitrary rates. Various design approaches are put into a unified framework to facilitate their comparison. To characterize the feasibility of the designs, the notion of distributed observability with respect to the graph of the network is introduced, which is akin to observability in centralized state estimation. It is concluded that a more general design procedure is desirable to reduce the size of exchanged information and to account for delays. The second contribution is the design of distributed observers where the estimates reach the state of the system exactly in a finite time, in contrast to the asymptotic convergence of the preceding linear designs. Sufficient bounds on the gain parameters are obtained using the concept of homogeneity. As a third contribution, an advantage of distributed observers is demonstrated by taking into account the specific effects of communications. In a numerical example, diffusively coupled observer nodes achieve a better performance compared to the direct transmission of partial outputs.
Présidente Mme Elena PANTELEY*, DR CNRS, HDR, L2S CentraleSupelec Rapporteurs Mr. Xiaomig HU, Professeur, KTH Stockholm, Suède Mr. Julien HENDRICKX, Professeur, UC Louvain, Belgique Examinateur Mr Panagiotis PATRINOS, Assistant Professor, KU Leuven, Co-Directeurs Mr. Wim MICHIELS, Professeur, KU Leuven (joint supervisor de la co-tutelle) Mr. Jean-Pierre RICHARD, Professeur, Centrale Lille Co-Directeurs invités Mme Rosane USHIROBIRA, Chargée de Recherche Inria, HDR Denis EFIMOV, Chargé de Recherche Inria, HDR
Thesis of the team VALSE defended on 10/07/2020