UCSD

Mechanical and Aerospace Engineering

• Home
• Publications
• Group
• Teaching
• Software
• Lab

---

The geometry behind invariance proximity: tight error bounds for Koopman-based approximations
M. Haseli, J. Cortés
Asian Journal of Control, submitted

Abstract

A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close it is to being invariant under the Koopman operator. The notion of invariance proximity provides a tight upper bound on the worst-case relative prediction error of the finite-dimensional model. This paper investigates the geometric structure behind the definition of invariance proximity, showing that this notion is a purely geometric object and can be defined solely in terms of Jordan principal angles on general inner product spaces. This geometric viewpoint provides a simple closed-form expression for invariance proximity which in turn can be computed by a myriad of existing algebraic methods in the literature.

pdf

Mechanical and Aerospace Engineering, University of California, San Diego
9500 Gilman Dr, La Jolla, California, 92093-0411

Ph: 1-858-822-7930
Fax: 1-858-822-3107

cortes at ucsd.edu
Skype id: jorgilliyo