Practical Guidelines for Data-driven Identification of Lifted Linear Predictors for Control

TL;DR

This paper provides practical guidelines for identifying lifted linear predictors (LLPs) using data-driven methods, enhancing their usability for control of nonlinear systems by improving the EDMD algorithm's effectiveness.

Contribution

It introduces practical, less intuitive guidelines for LLP identification with EDMD, supported by motivating examples and public implementation resources.

Findings

Guidelines improve LLP identification accuracy

Examples demonstrate practical application

Public repository supports reproducibility

Abstract

Lifted linear predictor (LLP) is an artificial linear dynamical system designed to predict trajectories of a generally nonlinear dynamical system based on the current state (or measurements) and the input. The main benefit of the LLP is its potential ability to capture the nonlinear system's dynamics with precision superior to other linearization techniques, such as local linearization about the operation point. The idea of lifting is supported by the theory of Koopman Operators. For LLP identification, we focus on the data-driven method based on the extended dynamic mode decomposition (EDMD) algorithm. However, while the EDMD algorithm presents an extremely simple and efficient way to obtain the LLP, it can also yield poor results. In this paper, we present some less intuitive practical guidelines for data-driven identification of the LLPs, aiming at improving usability of LLPs for designing control. We support the guidelines with two motivating examples. The implementation of the examples are shared on a public repository.