Posted January 15, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Saber Jafarpour, University of Colorado Boulder
tba
Posted November 10, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Rushikesh Kamalapurkar, University of Florida
Operator Theoretic Methods for System Identification
Operator representations of dynamical systems on Banach spaces provide a wide array of modeling and analysis tools. In this talk, I will focus on dynamic mode decomposition (DMD). In particular, new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems will be presented. In the SVD approach, 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 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 shown to be provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems are also discussed. This talk is based in part on joint works [RK23], [RK24], and [RRKJ24] with J.A. Rosenfeld.
Posted January 10, 2025
Last modified January 17, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Suhan Zhong, Texas A&M University
Polynomial Optimization in Data Science
Abstract: Optimization plays a pivotal role in data science. Recent advances in polynomial optimization have introduced innovative methods to solve many challenging problems in this field. In this talk, I will showcase the application of polynomial optimization through the lens of two-stage stochastic models. Additionally, I will provide a brief overview of the underlying theory and discuss potential future research directions.