About the speaker
Pauline Bernard graduated in Applied Mathematics from MINES ParisTech in 2014. She joined the Centre Automatique et Sytèmes of MINES ParisTech and obtained her Ph.D. in Mathematics and Control from Université PSL in 2017. For her work on observer design for nonlinear systems, she obtained the European Ph.D. award on Control for Complex and Heterogeneous Systems 2018. As a post-doctoral scholar, she then visited the Hybrid Systems Lab at the University California Santa Cruz, USA, and the Center for Research on Complex Automated Systems at the University of Bologna, Italy. In 2019, she became an assistant professor at the Centre Automatique et Sytémes of MINES ParisTech, Université PSL, France. Her research interests cover the observation and output regulation of nonlinear and hybrid systems.
Abstract
We review the main techniques of state observer design for continuous-time dynamical systems. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. In particular, we focus on the promising theory of KKL or nonlinear Luenberger observers which consists in transforming the dynamics into a linear filter of the output and where observability ensures the invertibility of the corresponding transformation. We will see how their use is also relevant in the more general case of non-observable systems where such algorithms still enable to reconstruct the observable partial information or even indistinguishable trajectories.