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Jean Auriol, PhD student at the Centre Automatique et Systèmes (CAS) of MINES ParisTech, in France, delivered a talk entitled "On robust control of linear coupled hyperbolic PDEs", at the Technical University of Crete on May 30th, 2018.
Abstract:
Linear first-order hyperbolic Partial Differential Equations represent a class of system that naturally arises in industrial processes where the dynamics involve a transport phenomenon. Due to this transport phenomenon, the stabilization of such systems is a challenging problem. Based on the example of a wave equation we show that uncertainties on the system parameters can lead to undesired phenomena. The analysis we propose is based on a rewrite of the system in the form of a neutral equation.
In the second part of this talk, we generalize the concepts previously introduced to solve the problem of robust stabilization for a system of two coupled linear hyperbolic PDEs. Using the backstepping method, we show that the solutions of this system can be rewritten as the solutions of a neutral equation (with distributed delays). The design of a stabilizing control law then becomes straightforward. We finally address some questions on the robustness properties of the designed control laws.
Short Bio:
Jean Auriol received his Master degree in civil engineering in 2015 (major: applied maths) in MINES ParisTech, part of PSL Research University. He started the same year his PhD at Centre Automatique et Systèmes of MINES ParisTech, part of the same university, under the direction of Florent Di Meglio. His PhD subject deals with robust control, observability and estimation design of hyperbolic Partial Differential Equations using a backstepping approach.
