Seminar by Akil Narayan
Speaker
Akil Narayan (University of Utah)
Title
Estimates for Hankel singular value decay of stable dynamical systems
Date
November 21, 2023 16:00 CET+0100 (Europe/Rome)
November 21, 2023 10:00 EST-0500 (US/Eastern)
November 21, 2023 09:00 CST-0600 (US/Central)
November 21, 2023 07:00 PST-0800 (US/Pacific)
Abstract
Projection-based (linear) model reduction for linear dynamical systems is an effective tool for capturing dynamics of large systems using parsimonious linear representations in a lower-dimensional space. There are myriad strategies for constructing such reduced-order models, and the effectiveness of reduced order modeling is often computationally analyzed by inspecting the decay or decay rate of the Hankel singular values of the system.
In this talk we’ll present new analysis for a straightforward greedy construction of a rational function approximation for the transfer function of stable large-scale dynamical systems. This new analysis, which immediately reveals corresponding algorithms, provides explicit rational approximability estimates of transfer functions in the H-infinity norm. The estimates involve sectorial properties of the system matrices, which provide a quantification of notions of dissipation-dominance or transport-dominance in dynamical systems. The theoretical constructions correspond to explicit Galerkin projection-based reduced order models of the original system, and hence this analysis provides concrete estimates of Hankel singular value decay. The framework we discuss is a paradigm that forges concrete relationships between rational approximation, Kolmogorov n-widths, and Galerkin projection-based model reduction.
Recording
Watch the recording on our YouTube channel.