Françoise Lamnabhi-Lagarrigue
(CNRS-L2S, CentraleSupelec, Universite Paris-Saclay)

Observer design for systems containing PDEs

ABSTRACT

Practical implementations of control systems need an online measurement of one or several physical variables. In simple control problems, where a few standard variables need to be measured online, the usual practice is to use hardware sensors. This hardware-sensor-based approach becomes rapidly impractical when facing more complex problems. First, sensors do not exist for non-standard variables (e.g. high-order derivatives of physical variables). Second, the implementation of a large number of sensors entails higher realization and maintenance costs and lower reliability. The modern approach consists in replacing hardware sensors by low cost and reliable software packages, called observers, designed on the basis of the models of the controlled systems. Intensive research activity has been devoted, especially over the last two decades, to observers and output feedback controllers (i.e., `observer-based controllers') leading to several efficient design approaches. This research effort has mainly been focused on nite dimensional systems described by ordinary differential equations (ODEs). However, the developed approaches do not apply to the numerous real-life physical systems which are distributed both in space and time and are described by Partial Differential Equations (PDEs). In this talk, based on a similar idea than a result from Germani, Manes and Pepe for dealing with delays for nite-dimensional systems, by using a set of chained predictors simultaneously operating, an observer will be here designed for a class of nonlinear parabolic PDEs with delayed point measurements. The novelty lies is that the delay size is arbitrary. To compensate for this arbitrary delay effect, the observer will consist of several chained sub-observers. Each sub-observer compensates a fraction of the global delay. The resulting estimation error system will be shown to be exponentially stable provided that a sufficient number of sub-observers is used. The stability analysis is based on a speci c Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of LMIs.


ABOUT THE SPEAKER

Françoise Lamnabhi-Lagarrigue, IFAC Fellow, is CNRS Senior Researcher since 1993 at the Laboratoire des Signaux et Systemes. She obtained the Master of
Mathematics degree at the University Paul Sabatier (Toulouse) in 1976 and she held a CNRS researcher position in 1980. She received her Ph.D. and Habilitation
Doctorate degrees (Docteur d'etat des Sciences Physiques) from the University Paris Sud in 1980 and 1985, respectively. Some recent activities include: Senior
Area Editor of International Journal of Control (Taylor & Francis); Scienti c Manager of the Marie Curie Control Training Site, CTS (ended December 2006);
Elected Member of the Board of Governors of the IEEE Control Systems Society for 2003-2005; Scienti c Manager of the HYCON Network of Excellence (ended
March 2009) and HYCON2 (2010-2014); Since 2010, she is member of the Executive Committee of GdR MACS. She is the founder of the European Embedded
Control Institute (EECI) and the chair of the EECI International Graduate School on Control. She was serving as Member of the IFAC Technical Board, as Chair of
CC9 Social Systems, during the triennium (2011 to 2014) and (2014 to 2017). Her main recent research interests include observer design, performance and
robustness issues in nonlinear, hybrid, networked and distributed control systems. She has supervised 26 PhD thesis. She is author of 1 book, editor or co-editor of 11 books and 5 Special Issues; she is author and co-author of 106 journal papers and chapters of books, 118 published international conference papers and 1 patent ( led in 2018). She is the prizewinner of the 2008 Michel Monpetit prize of the French Academy of Science, of the 2010-2013 Prime d'Excellence Scienti que
at CNRS and of the 2014 IFAC NMO France. From January 2014 to February 2016 she was deputy director of the Ecole Doctorale STIC of the University of
Paris-Saclay. She was appointed member (2013-2018) of the Scienti c Council of the Institute for Information Science and interactions (CNRS-INS2I). She is
member of the Programme Committee of the ITE SuperGrid and Editor-in-Chief of Annual Reviews in Control (Elsevier) since 2016. She was nominated member
of the Board of Governors of the IEEE CSS for the year 2016 and she is elected member for 2018-2020. Since April 2016, she is a knight of the Legion of Honor.