Data-Driven Modeling and Estimation of Dynamical Systems
The long term goal of this project is to apply tools from Markov operator theory, including the Koopman and Perron-Frobenius operators, to the problem of adaptive sampling of geospatial processes. This project will address fundamental questions on how to select optimal locations to collect observations and how to ensure that sensor platforms travel to these locations along informative paths. The significance of the proposed research lies in the observation that climate processes occur on long time scales. Understanding these processes requires a combination of models and observations, which can be collected over large space-time volumes by fleets of high-endurance autonomous vehicles that steer intelligently to maximize the utility of their measurements. For example, underwater vehicles that sample the ocean interior are important for understanding ocean processes in general, because -- unlike weather prediction in the atmosphere -- the subsurface ocean environment is difficult to sample remotely. The goal of this project is to create new path-planning strategies for unmanned, mobile sensor platforms to measure information-rich but undersampled spatiotemporal processes. Participants will apply tools from data assimilation, nonlinear control, and dynamical systems theory.
Professor Paley has worked with over a dozen undergraduate students in his Collective Dynamics and Control Laboratory, including three TREND students.