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 several class of PDEs 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);
- Boundary observer design; Boundary control of hyperbolic PDEs (wave);
- Control of first-order hyperbolic PDEs and delay equations.
Mamadou Diagne received the Ph.D. degree in 2013 at Laboratoire d’Automatique et du Génie des Procédés, Université Claude Bernard Lyon I. He ´ has been a postdoctoral fellow at the Cymer Center for Control Systems and Dynamics of University of California San Diego from 2013 to 2015 and at the Department of Mechanical Engineering of the University of Michigan from 2015 to 2016. He is currently an Assistant Professor at Rensselaer Polytechnic Institute. His research interests concern the modeling and the control of heat and mass transport phenomena, production/manufacturing systems and additive manufacturing processes described by partial differential equations and delay systems.