In the first part of this talk, I will present work on data-driven system identification, a mathematically sound, system-theoretic way to obtain models from experimental or simulated data. We propose a method that enables subspace-based system identification for large-scale data via a maximum-volume based CUR algorithm. The CUR decomposition is a state-of-the-art method for compressing matrices by exploiting low-rank structure. The proposed approach does not require loading all data into fastmemory. We present a worst-case error bound and discuss computational advantages of our approach, for instance, over 100x performance gains are realized on a numerical example.
In the second part of the talk, I will discuss recent results on control of systems with uncertain time-varying parameters. In this setting, designing an optimal feedback controller is complicated by the fact that these system parameters are unknown. Thus, we propose to learn reduced-order models from system data that can then be used for reduced-order feedback control. The method recognized changes in the underlying parameters, and initiates a model learning step. The derived data-driven controllers successfully stabilize the considered convection-diffusion equation.