BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.4.0.1//EN TZID:America/New_York X-WR-TIMEZONE:America/New_York BEGIN:VEVENT UID:0-6445@eng.ufl.edu DTSTART;TZID=America/New_York:20240229T124500 DTEND;TZID=America/New_York:20240229T134500 DTSTAMP:20251201T210350Z URL:https://www.eng.ufl.edu/news-events/events/mae-seminar-operator-theore tic-methods-for-data-driven-modeling-and-control/ SUMMARY:MAE Seminar - Operator Theoretic Methods for Data-Driven Modeling a nd Control DESCRIPTION:MAE Seminar - Operator Theoretic Methods for Data-Driven Modeli ng and Control\nThursday\, February 29\, 2024\, at 12:50pm\, Location: MAE -A 303\nDr. Rushikesh Kamalapurkar\, Associate Professor\, School of Mecha nical and Aerospace Engineering\, Oklahoma State University\nAbstract\nIn an effort to automate increasingly complex cyber-physical systems\, where first-principles models of the underlying physical processes are either po orly 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 qu estions that need to be answered to solidify the theoretical foundations o f data-driven control. The research in my lab has been motivated by the ne ed to develop theoretically sound ways to include insights gained from dat a into modeling\, decision\, and control architectures. Over the past deca de\, the study of dynamical systems as operators acting on spaces of funct ions 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 accompanyi ng theoretical guarantees have either been weak\, or have required strong assumptions that do not hold for large classes of dynamical systems.\nIn t his talk\, I will present new results on provably convergent singular valu e decomposition (SVD) of total derivative operators corresponding to dynam ic 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 dynamic al systems provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operator s that converges\, in norm\, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given samp le trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and le ft singular functions of the finite rank operators to those of the total d erivative operator. Finally\, the convergent SVDs are utilized to construc t estimates of the vector field that models the system. The estimated vect or fields are provably convergent\, uniformly on compact sets. Extensions to systems with control and to partially unknown systems will also be disc ussed.\nBiography\nRushikesh Kamalapurkar received his M.S. and his Ph.D. degrees in 2011 and 2014\, respectively\, from the Department of Mechanica l and Aerospace Engineering at the University of Florida. After working fo r a year as a postdoctoral researcher with Dr. Warren E. Dixon\, he was ap pointed 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 prim ary 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.\nMAE Faculty Host: Dr. Yu Wang CATEGORIES:Seminars LOCATION:MAE-A Room 303\, 939 Sweetwater Drive\, Gainesville\, FL\, 32611\, United States GEO:29.643814;-82.34865 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=939 Sweetwater Drive\, Gain esville\, FL\, 32611\, United States;X-APPLE-RADIUS=100;X-TITLE=MAE-A Room 303:geo:29.643814,-82.34865 END:VEVENT BEGIN:VTIMEZONE TZID:America/New_York X-LIC-LOCATION:America/New_York BEGIN:STANDARD DTSTART:20231105T010000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST END:STANDARD END:VTIMEZONE END:VCALENDAR