Space-Filling Input Design for Nonlinear State-Space Identification

TL;DR

This paper proposes a space-filling input design method for nonlinear state-space system identification, ensuring comprehensive exploration of the operation range to improve model quality and robustness.

Contribution

It introduces a novel experiment design approach for nonlinear systems that emphasizes full operation range coverage, extendable to various system classes.

Findings

Effective design for nonlinear mass-spring-damper system

Utilizes multisine input signals for experiment planning

Enhances data informativity for nonlinear system modeling

Abstract

The quality of a model resulting from (black-box) system identification is highly dependent on the quality of the data that is used during the identification procedure. Designing experiments for linear time-invariant systems is well understood and mainly focuses on the power spectrum of the input signal. Performing experiment design for nonlinear system identification on the other hand remains an open challenge as informativity of the data depends both on the frequency-domain content and on the time-domain evolution of the input signal. Furthermore, as nonlinear system identification is much more sensitive to modeling and extrapolation errors, having experiments that explore the considered operation range of interest is of high importance. Hence, this paper focuses on designing space-filling experiments i.e., experiments that cover the full operation range of interest, for nonlinear dynamical systems that can be represented in a state-space form using a broad set of input signals. The presented experiment design approach can straightforwardly be extended to a wider range of system classes (e.g., NARMAX). The effectiveness of the proposed approach is illustrated on the experiment design for a nonlinear mass-spring-damper system, using a multisine input signal.