**10:00-11:00 Jean Auriol** (Chargé de recherche, CNRS, L2S, CentraleSupélec)

**Title.** Robust backstepping stabilization of linear hyperbolic PDEs systems. Application to a drilling problem.

**Abstract. **Linear hyperbolic systems naturally arise when modeling industrial processes for which the dynamics involve a transport phenomenon (related applications include electric transmission lines, traffic flow, oil well drilling…). These systems are the source of complex control and engineering problems (mostly due to the transport phenomena and the presence of destabilizing terms), which have impact in terms of environmental safety and economic feasibility. In this presentation, we develop operating methods for the control of such hyperbolic systems. More precisely, using a backstepping approach combined with a rewrite of the system as a difference equation, we design an explicit control law (and the corresponding dual observer) that guarantees the robust output feedback stabilization of a system of two hyperbolic PDEs. The proposed control law introduces three degrees of freedom (by means of tuning parameters) that enable a trade-off between performance and robustness, between disturbance rejection and sensitivity to noise. The proposed approach can be extended to higher dimensional systems and networks interconnected systems. Finally, we conclude this presentation by considering the problem of toolface control for directional drilling operations with the bit off-bottom. The torsional dynamics of such a system can be modeled as a non-linear hyperbolic system for which a robust backstepping-based state-observer is designed to monitor at all times the torque and the RPM. Using these estimations, we design an algorithm that controls the toolface orientation. The different algorithms are tested against real field data.

**Biography.** Jean Auriol received his Master degree in civil engineering in 2015 (major: applied maths) in MINES ParisTech, part of PSL Research University and in 2018 his Ph.D. degree in control theory and applied mathematics from the same university (Centre Automatique et Systèmes). His Ph.D. thesis, entitled Robust design of backstepping controllers for systems of linear hyperbolic PDEs, has been nominated for the best thesis award given by the GDR MACS and the Section Automatique du Club EEA in France. From 2018 to 2019, he was a Posdoctoral Researcher at the Department of Petroleum Engineering, University of Calgary, AB, Canada, where he was working on the implementation of backstepping control laws for the attenuation of mechanical vibrations in drilling systems. From December 2019, he is a Junior Researcher (Chargé de Recherches) at CNRS, Université Paris-Saclay, Centrale Supelec, Laboratoire des Signaux et Systèmes (L2S), Gif-sur-Yvette, France.His research interests include robust control of hyperbolic systems, neutral systems, networks and interconnected systems.

**11:00-12:00 Federico Bribiesca-Argomedo** (Associate Professor, Department of Mechanical Engineering, Institut National des Sciences Appliquées de Lyon)

**Title.** Handling interconnections in hyperbolic-PDE/ODE systems with reduced over-actuation.

**Abstract.** Linear hyperbolic PDEs are a common representation for natural or artificial processes where some quantity: matter, energy, information, etc., propagates with a finite speed on a spatial, or at least space-like, domain. In particular, systems of coupled hyperbolic PDEs are a common occurrence, since balance laws rarely appear in an isolated manner, and information in a system (e.g., the effect of actuation on a process) tends to propagate in all, or at least several, spatial directions. In this talk we will focus on the use of the infinite-dimensional backstepping method to simplify coupling structures in systems of hyperbolic PDEs, allowing for constructive control designs that do not require the use of « one actuator per transport equation, » thus reducing the need for over-actuated systems. The focus will be on results showing how the method extends to cases where ODE dynamics are present on the actuated and/or unactuated boundaries of hyperbolic systems. Particular attention will be paid to the robustness of such designs, which can require an « infinite bandwidth » in their more naive forms, with respect to small delays in the control loop. A more practical control design will be presented, using adequately designed filters to restrict the bandwidth of the resulting controller while preserving the stability of the closed-loop system.

**Biography.**Federico Bribiesca-Argomedo received the B.Sc. degree in mechatronics engineering from the Tecnológico de Monterrey, Monterrey, Mexico, in 2009, the M.Sc. degree in control systems from Grenoble INP, Grenoble, France, in 2009, and the Ph.D. degree in control systems from GIPSA-Laboratory, Grenoble University, Grenoble. He held a post-doctoral position with the Department of Mechanical and Aerospace Engineering, University of California, San Diego, San Diego, CA, USA. He is currently an Associate Professor with the Department of Mechanical Engineering, Institut National des Sciences Appliquées de Lyon, Lyon, France, attached to Ampère Laboratory. Research interests include control of hyperbolic and parabolic partial differential equations and nonlinear control theory. Past and current applications include tokamak safety factor profiles, electrochemical models of Li-ion batteries and energy distribution networks.