Precision Data-enabled Koopman-type Inverse Operators for Linear Systems

TL;DR

This paper develops a data-driven method to accurately invert linear system dynamics by incorporating output history and derivatives, effectively removing hidden state dependencies for improved precision.

Contribution

It introduces a novel approach that identifies the necessary output history and derivatives to eliminate hidden state effects in Koopman-type inverse operators for linear systems.

Findings

Inclusion of output history and derivatives enhances inverse operator accuracy.

The method successfully removes hidden state dependence in linear systems.

Illustrated with an example demonstrating improved precision.

Abstract

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the dynamics can also depend on hidden states that are not directly measured. The main contribution of this work is to identify the information needed (in particular, the past history of the output) to remove the hidden state dependence in Koopman-type inverse operators for linear systems. Additionally, it is shown that the time history of the output should be augmented with the instantaneous time derivatives of the output to achieve precision of the inverse operator. This insight into the required output (history and instantaneous derivative) information, to remove the hidden-state dependence and improve the precision of data-enabled inverse operators, is illustrated with an example system.