MINES ParisTech CAS - Centre automatique et systèmes

Feedback control of 1D hyperbolic systems

Thursday 30th September 2021, 4pm – 5pm.

Amaury Hayat, CERMICS, Ecole des Ponts ParisTech, France

In this talk we study the feedback control of 1D hyperbolic systems. We first investigate what can be done for nonlinear systems with a direct Lyapunov approach using energy-like Lyapunov functions. We look in particular at the special case of density-velocity systems, a class that encompasses many physical equations in physics and mechanics. Then, we present an extraction method to deal with nonlinear systems using a boundary PI control. Finally, we look at an example of a system where such methods cannot be used, and more advanced techniques are needed. We present a backstepping approach which consists in finding an invertible mapping between this system and a system much simpler to stabilize. Instead of using the usual Volterra transform involved in most of the backstepping literature, we look at more generic transforms. This allows more powerful results but also brings new difficulties.

Amaury Hayat received the engineering degree from Ecole Polytechnique, France, in 2014, the master’s degree in mathematics from the University of Cambridge, U.K. in 2015, and from the Corps des Ponts, des Eaux et des Forêts, France in 2016. He received the Ph.D. degree in 2019 from Sorbonne Université, France under the supervision of Jean-Michel Coron. In 2019-2020 he was a research associate at Rutgers University-Camden, and he is currently an assistant professor at Ecole des Ponts Paristech.