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Join us as Debdipta Goswami shares about Unveiling the Impact of Limited Bandwidth on Koopman-Based Identification and Control.

Professor Debdipta Goswami joined the Department of Mechanical and Aerospace Engineering, the Ohio State University, in 2022 as an assistant professor. His research interests lie at the intersection of control systems and machine learning with a focus on motion planning and agile control of aerial robots. He has worked on data-driven discovery and control of dynamical systems using operator-theoretic methods and reservoir computers. His current research focuses on the structured learning of control systems from data with guaranteed performance and simultaneous learning and control of dynamical systems.

Abstract

Koopman-based data-driven algorithms, such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD), have gained popularity over the past decade as system identification techniques for model predictive control (MPC). However, these methods implicitly assume high-quality data for training, which may not be feasible in many real-world scenarios. For instance, an unmanned micro-air vehicle (UMAV) mapping its environment may transmit sensor data to an edge server, where system identification and learning occur. This data transmission can be affected by bandwidth constraints, channel noise, and packet loss. In this talk, we investigate the impact of bandwidth constraints, specifically quantization, on the identification and learning processes using Koopman-based methods. We will explore the fundamental relationship between estimates of the Koopman operator derived from unquantized data and those obtained from quantized data through DMD/EDMD. Furthermore, utilizing the law of large numbers, we demonstrate that, in a large data regime, the quantized estimate can be regarded as a regularized version of the unquantized estimate. We also examine the relationship between the two estimates in the finite data regime and analyze how nonlinear lifting functions influence this regularization due to quantization. Additionally, we demonstrate how the performance of data-driven MPC deteriorates as a result of quantization in controlled dynamical systems with an application in aerial robotics.