DIFFER Seminar: Making multi-physics a piece of PIE

Abstract: Multi-physics processes - such as heat flow, fluid dynamics, and electrical systems - are naturally described by Partial Differential Equations (PDEs). These mathematical models capture how physical quantities change over both space and time. However, PDEs are notoriously difficult to handle because their solutions exist in infinite-dimensional spaces, making computations and control design very challenging. Traditionally, engineering problems are solved by approximating these complex equations using numerical methods, reducing them to finite models so they can be solved on a computer. While this makes design and simulation easier, it also introduces a serious limitation: controllers based on these approximations may not work well - or at all - when applied to the original PDE system. The mismatch between the approximate model and the true, infinite-dimensional system can lead to poor performance or even failure in real-world applications. In this presentation, I will introduce a new control framework - PIE (Partial Integral Equation) - that allows us to work directly with the original PDE models, without needing any prior numerical approximation. With this approach, controllers are synthesized to be valid for the actual, infinite-dimensional system, ensuring both reliability and robustness when applied to real multi-physics processes. This bypasses many pitfalls of traditional methods and opens the door to safer, more effective control of complex physical systems.

Bio: Amritam Das received MSc. degree (2016) in Systems and Control and Ph.D. degree (2020) in Electrical Engineering from Eindhoven University of Technology. He held the position of research associate at the the University of Cambridge (2020-2021) where he was affiliated with Sideny Sussex College as a college research associate. During 2021-2023, he was a post-doctoral researcher at KTH Royal Institute of Technology. Since February 2023, He is now working an assistant professor at the Control Systems group of Eindhoven University of Technology. He serves as an associate editor for the European Journal of Control and a member of the IEEE CSS conference editorial board. He is also a member of IEEE/IFAC Technical Committee on Distributed Parameter Systems and Network Systems. His research interests are nonlinear control, physics-informed learning, control of PDEs, and model reduction.