Linear Matrix Inequality Approaches to Koopman Operator Approximation

TL;DR

This paper introduces a convex optimization framework using linear matrix inequalities to approximate the Koopman operator from data, enabling the incorporation of stability and regularization constraints.

Contribution

It formulates the Koopman operator approximation as an LMI-constrained convex optimization problem, allowing flexible inclusion of stability and regularization constraints.

Findings

Enables incorporation of stability constraints into Koopman approximation

Allows regularization using matrix and system norms

Provides a flexible convex optimization framework for data-driven Koopman analysis

Abstract

The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered. The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI) constraints. Doing so allows for additional LMI constraints to be incorporated into the regression problem. In particular, asymptotic stability constraints, regularization using matrix norms, and even regularization using system norms can be easily incorporated into the regression problem.