Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. Generally, key aspects of these processes operating mode are driven by convection phenomena with a spatiotemporal dynamic that cannot be approximated straightforwardly using a finite-dimensional representation. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.
The topics we will cover:
- Lyapunov stability;
- Exact Solutions to PDEs;
- Boundary control of parabolic PDEs (reaction-advection-diffusion);
Mamadou Diagne is currently an Assistant Professor in the Department of Mechanical Aerospace and Nuclear Engineering at Rensselaer Polytechnic Institute. He received his Ph.D. degree in 2013 at the Laboratory of Automatic Control, Chemical and Pharmaceutical Engineering of the University Claude Bernard Lyon I (France). He was first a postdoctoral fellow at the Cymer Center for Control Systems and Dynamics of UC San Diego from 2013 to 2015 and then at the Department of Mechanical Engineering of the University of Michigan from 2015 to 2016. His research interests concern the modeling of flow systems involving heat and mass transport phenomena and the control of PDEs, mixed PDE/ODEs, and delay systems. He received the NSF CAREER in 2020 and the Graduate Assistance in Area of National Need grant from the Department of Education in 2018.