Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems
Systems and Control
2022-03-02 v2 Systems and Control
Optimization and Control
Abstract
Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems'. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.
Cite
@article{arxiv.2103.16171,
title = {Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems},
author = {Chris Verhoek and Roland Tóth and Sofie Haesaert and Anne Koch},
journal= {arXiv preprint arXiv:2103.16171},
year = {2022}
}
Comments
Accepted to the 60th Conference on Decision and Control 2021 (CDC2021)