MAE Seminar – Operator Theoretic Methods for Data-Driven Modeling and Control

Details

MAE Seminar – Operator Theoretic Methods for Data-Driven Modeling and Control

Thursday, February 29, 2024, at 12:50pm, Location: MAE-A 303

Dr. Rushikesh Kamalapurkar, Associate Professor, School of Mechanical and Aerospace Engineering, Oklahoma State University

Abstract
In an effort to automate increasingly complex cyber-physical systems, where first-principles models of the underlying physical processes are either poorly understood or computationally taxing, practitioners have gravitated towards data-driven modeling and control techniques such as. However, the fast pace of adaptation has resulted in a plethora of open theoretical questions that need to be answered to solidify the theoretical foundations of data-driven control. The research in my lab has been motivated by the need to develop theoretically sound ways to include insights gained from data into modeling, decision, and control architectures. Over the past decade, the study of dynamical systems as operators acting on spaces of functions has resulted in promising tools, such as Carleman lifting, dynamic mode decomposition, and their variants, for modeling and control. While the tools have proven effective in many application areas, the accompanying theoretical guarantees have either been weak, or have required strong assumptions that do not hold for large classes of dynamical systems.

In this talk, I will present new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems. Dynamic systems are modeled as total derivative operators that operate on reproducing kernel Hilbert spaces (RKHSs). The resulting total derivative operators are shown to be compact for a large class of dynamical systems provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operators that converges, in norm, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given sample trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and left singular functions of the finite rank operators to those of the total derivative operator. Finally, the convergent SVDs are utilized to construct estimates of the vector field that models the system. The estimated vector fields are provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems will also be discussed.

Biography
Rushikesh Kamalapurkar received his M.S. and his Ph.D. degrees in 2011 and 2014, respectively, from the Department of Mechanical and Aerospace Engineering at the University of Florida. After working for a year as a postdoctoral researcher with Dr. Warren E. Dixon, he was appointed as the 2015-16 MAE postdoctoral teaching fellow. In 2016 he joined the School of Mechanical and Aerospace Engineering at the Oklahoma State University, where he currently serves as an associate professor. His primary research interests are data-driven modeling and learning-based optimal control of uncertain nonlinear dynamical systems. He has published a book, multiple book chapters, over 35 peer reviewed journal papers and over 35 peer reviewed conference papers.

MAE Faculty Host: Dr. Yu Wang