Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

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.

Accepted to the 60th Conference on Decision and Control 2021 (CDC2021)

References in corpus (1)

• Data-Driven Predictive Control for Linear Parameter-Varying Systems

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• Decoupling parameter variation from noise: Biquadratic Lyapunov forms in data-driven LPV control
• A quantitative and constructive proof of Willems' Fundamental Lemma and its implications
• Data-based system representations from irregularly measured data
• Online Data-Driven Adaptive Control for Unknown Linear Time-Varying Systems
• Direct data-driven control of LTV systems
• A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs
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