In this lecture we will address the problem of observer design for nonlinear systems. It is mainly devoted to Linear Matrix Inequality (LMI) based methods and their use to improve observer design for a large class of nonlinear systems. A second part of this course will be dedicated to simple but useful contributions to high-gain observer design, where some techniques to improve performances of the standard high gain observer will be presented.
Before tackling the problem of observer design, basic notions on stability by using direct and indirect Lyapunov methods will be thoroughly discussed. An introduction to observability (with simple interesting examples) and a short state of the art on different available methods on observer design will be recalled.
Dr. Khadidja Chaib Draa will show an important application of the LMI-based techniques on estimation of certain variables in anaerobic digestion processes. A thorough presentation of a biogas model and simulations by using Matlab will be provided. Other applications will also be discussed. If we have time, some new advanced estimation algorithms will be presented.
Ali Zemouche received his Ph.D. degree in automatic control in 2007, from the University Louis Pasteur, Strasbourg, France, where he held post-doctorate degree from October 2007 to August 2008. Dr. Zemouche joined, as Associate Professor, the Centre de Recherche en Automatique de Nancy at Université de Lorraine, since September 2008. He held an academic position at Inria – Saclay (EPI DISCO) from September 2016 to August 2017. His research activities include nonlinear systems, state observers, observer-based control, time-delay systems, robust control, learning-based methods, and application to real-world models. Dr. Zemouche is currently associate editor in international journals: SIAM Journal of Control and Optimization, IEEE Transactions on Automatic Control, Automatica, European Journal of Control, and IEEE Systems Journal. He is also a member of the Conference Editorial Board of IEEE Control Systems Society and IFAC TC2.3 (Non-Linear Control Systems).
Khadidja Chaïb Draa obtained her PhD degree, in engineering science, from University of Luxembourg and University of Lorraine. After her graduation, she created the start-up company ‘TechnOptiz’ in order to jump and build a bridge between research and industrial applications. Her purpose is to tune academic ideas into a real business. She is also the scientific adviser of the biogas association in Luxembourg ‘Biogasvereenegung’ and she gives lectures at the University of Luxembourg. Although she works in her start up, she is a researcher at heart; her research interests include nonlinear observer design, LPV systems, LMIs, and anaerobic digestion.