On excitation of control-affine systems and its use for data-driven Koopman approximants

TL;DR

This paper introduces a new data-fitting framework for control-affine systems that enhances the robustness of bilinear EDMD models, enabling more reliable data-driven control of complex dynamical systems.

Contribution

It proposes a novel approach for input selection and optimality conditions to improve bilinear EDMD robustness in control-affine system identification.

Findings

Improved robustness margins in bilinear EDMD models.

Guidelines for input selection based on subspace angles.

Successful application to non-holonomic robots.

Abstract

The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework for data-fitting of control-affine mappings to increase the robustness margin in the associated system identification problem and, thus, to provide more reliable bilinear EDMD schemes. In particular, guidelines for input selection based on subspace angles are deduced such that a desired threshold with respect to the minimal singular value is ensured. Moreover, we derive necessary and sufficient conditions of optimality for maximizing the minimal singular value. Further, we demonstrate the usefulness of the proposed approach using bilinear EDMD with control for non-holonomic robots.