Séminaire d'Automatique du plateau de Saclay

Séminaire le 17 Octobre 2019, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Islam Boussaada & Ludovic Sacchelli

10:00-11:00 Islam Boussaada (Inria Saclay, Equipe DISCO & L2S, Gif-Sur-Yvette)

Title: Coalescence and Splitting Mechanisms of Spectral Values and their Effect on Stability: Towards a New Framework for Reduced Complexity Pole-placement Design for Time-Delay Systems

Abstract: For linear delay-differential equations, a question of ongoing interest is to determine conditions on the equation parameters that guarantee exponential stability and stabilization of solutions. This talk starts by a review of an old design method for time-delay systems called finite pole-placement. Its advantages and limitations shall be stressed. Next, some recent results showing a link between the stable manifold and the manifold corresponding to a given multiplicity of a spectral value shall be presented, hence enabling a spectral abscissa assignment. After a motivation of the tracking of multiple spectral values for analysis/control perspectives, some existing links between Birkhoff’s interpolation problem and a result due to Pólya and Szegö on the number of quasipolynomial's roots in a horizontal strip shall be revisited. Later, hints of an analytic proof of the dominancy of the quasipolynomial's root will be presented, setting up a reduced-complexity delayed stabilizing design. Sensitivity of the control design with respect to the parameters' variation will be discussed. To overcome the sensitivity of multiple roots, an extension of the approach to real distinct pole assignment shall be presented. Finally, various reduced order examples will illustrate the applicative perspectives of the proposed control approach.

Biography: Islam Boussaada received his Master in Mathematics from University Tunis II, and an M.Sc. degree in Pure Mathematics from University Paris 7 in 2004. In December 2008, he defended his Ph.D. degree in Mathematics from University of Rouen Normandy. In June 2016, he received his HDR degree (French Habilitation) in Physics from University Paris Saclay-University Paris Sud. In 2010, IB was appointed for two years as a post-doctoral fellow in the control of time-delay systems at L2S, Supelec-CNRS-University Paris Sud. Since 2012, he has been an associate professor at IPSA and an associate researcher at MODESTY Team of L2S. Since September 2017, IB is appointed permanent researcher at DISCO Team and full professor at IPSA where he headed the Aeronautical and Aerospace Systems department from September 2017 till May 2019.
Since September 2018 untill August 2020, IB is a researcher in temporary secondment at Inria Saclay-DISCO Team. His research interests belong to the qualitative theory of dynamical systems and its application in control problems. It includes stability analysis and stabilization of linear/nonlinear dynamical systems, analysis of parametric systems, analysis of delay induced dynamics, nonhyperbolic dynamics, analysis of algebraic dierential systems, control of active vibrations, dynamics of biochemical networks. IB is co-author of a monograph and co-editor of a contributed book, both published in Springer series, as well as co-author of more than 60 peer-reviewed publications. He co-organized the 4th GDRI DelSys's Workshop on Observing and Controlling Complex Dynamical Systems (November 2015), as well as the 1st GDRI Spa-Disco's workshop on Delays and Constraints in Distributed Parameters Systems (November 2017), both funded by CNRS and held at CentraleSupelec (Gif sur Yvette). At the occasion of the 20th World Congress of the International Federation of Automatic Control (IFAC) (Toulouse, July 2017), IB co-organized an invited session "Frequency domain Techniques for Time-delay Systems". At the occasion of the 13th-15th IFAC Workshop on Time-delay Systems (Istanbul 2016, Budapest 2018, Sinaia 2019), IB co-organized thematic sessions on Spectral Methods for Rightmost Roots Characterization in LTI Time-delay Systems. Since September 2018, IB is co-leading the national research group GT OSYDI of the CNRS/GDR MACS and is a deputy director of the IRS iCODE Institute of the University Paris Saclay.

11:00-12:00 Ludovic Sacchelli (Lehigh University, Pennsylvania, USA)

Title: Stabilization of non-uniformly observable system


Abstract: A common strategy in dynamic output feedback stabilization is to apply a state feedback to an observer in order to stabilize the coupled state-observer system. It is well known that global stabilizability, paired with uniform observability, implies semi-global stabilisability by dynamic output feedback. However in many generic cases, the system is not uniformly observable, and usual strategies for semi-global stabilization break down. New approaches need to be explored to resolve this issue. We will present case studies to give an outlook for the challenges raised by this problem and highlight a promising answer based on the idea of unitary embeddings of control systems.

Biography: Ludovic Sacchelli is a visiting assistant professor in the Mathematics Department of Lehigh University, in Bethlehem, Pennsylvania. He graduated from Ecole Normale Supérieure de Cachan and received his master's degree in analysis of PDEs from Paris-Sud University in 2015. He obtained a Ph.D. in applied mathematics from Ecole Polytechnique in 2018 on the topic of sub-Riemannian geometry. Ludovic spent the following year as a postdoc in the Electrical Engineering Department of University of Toulon (LIS Lab) before departing for his current position. His research interests lie in sub-Riemannian geometry, control theory and observability.