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Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect…

Systems and Control · Electrical Eng. & Systems 2023-08-14 Guanru Pan , Ruchuan Ou , Timm Faulwasser

The fundamental lemma by Jan C. Willems and co-authors enables the representation of all input-output trajectories of a linear time-invariant system by measured input-output data. This result has proven to be pivotal for data-driven…

Systems and Control · Electrical Eng. & Systems 2024-11-06 Guanru Pan , Ruchuan Ou , Timm Faulwasser

Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this…

Systems and Control · Electrical Eng. & Systems 2023-08-04 Guanru Pan , Ruchuan Ou , Timm Faulwasser

We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…

Systems and Control · Electrical Eng. & Systems 2025-10-07 Johannes Teutsch , Sebastian Kerz , Dirk Wollherr , Marion Leibold

The fundamental lemma by Willems and coauthors facilitates a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays an important role in data-driven simulation and…

Optimization and Control · Mathematics 2022-05-16 Jeremy Coulson , Henk van Waarde , Florian Dörfler

Willems' fundamental lemma and system level synthesis both characterize a linear dynamic system by its input/output sequences. In this work, we extend the application of the fundamental lemma from deterministic to uncertain LTI systems and…

Systems and Control · Electrical Eng. & Systems 2021-03-11 Yinghao Lian , Colin N. Jones

In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric…

Optimization and Control · Mathematics 2022-02-17 Philipp Schmitz , Timm Faulwasser , Karl Worthmann

Willems' Fundamental Lemma enables parameterizing all trajectories generated by a Linear Time-Invariant (LTI) system directly from data. However, this lemma relies on the assumption of noiseless measurements. In this paper, we provide an…

Systems and Control · Electrical Eng. & Systems 2026-04-02 Sahand Kiani , Constantino M. Lagoa

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…

Systems and Control · Electrical Eng. & Systems 2022-03-02 Chris Verhoek , Roland Tóth , Sofie Haesaert , Anne Koch

A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time invariant (LTI) systems with unknown dynamics purely from data. While most…

Systems and Control · Electrical Eng. & Systems 2023-03-28 Sebastian Kerz , Johannes Teutsch , Tim Brüdigam , Dirk Wollherr , Marion Leibold

Willems' fundamental lemma enables data-driven analysis and control by characterizing an unknown system's behavior directly in terms of measured data. In this work, we extend a recent frequency-domain variant of this result--previously…

Systems and Control · Electrical Eng. & Systems 2025-04-10 T. J. Meijer , M. Wind , V. S. Dolk , W. P. M. H. Heemels

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result,…

Optimization and Control · Mathematics 2024-07-18 Philipp Schmitz , Timm Faulwasser , Paolo Rapisarda , Karl Worthmann

The fundamental lemma by Jan C. Willems and co-workers, which is deeply rooted in behavioral systems theory, has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style…

Optimization and Control · Mathematics 2023-05-01 Timm Faulwasser , Ruchuan Ou , Guanru Pan , Philipp Schmitz , Karl Worthmann

The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control…

Systems and Control · Electrical Eng. & Systems 2022-12-16 Guanru Pan , Ruchuan Ou , Timm Faulwasser

The Willems' fundamental lemma, which characterizes linear dynamics with measured trajectories, has found successful applications in controller design and signal processing, which has driven a broad research interest in its extension to…

Optimization and Control · Mathematics 2021-06-01 Yingzhao Lian , Colin N. Jones

Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that…

Systems and Control · Electrical Eng. & Systems 2021-04-13 Yue Yu , Shahriar Talebi , Henk J. van Waarde , Ufuk Topcu , Mehran Mesbahi , Behçet Açıkmeşe

Recent years have witnessed a booming interest in data-driven control of dynamical systems. However, the implicit data-driven output predictors are vulnerable to uncertainty such as process disturbance and measurement noise, causing…

Optimization and Control · Mathematics 2024-07-08 Yibo Wang , Keyou You , Dexian Huang , Chao Shang

We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…

Systems and Control · Computer Science 2020-04-09 Tuhin Sarkar , Alexander Rakhlin , Munther A. Dahleh

Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…

Systems and Control · Electrical Eng. & Systems 2024-04-25 Nathan P. Lawrence , Philip D. Loewen , Shuyuan Wang , Michael G. Forbes , R. Bhushan Gopaluni

Willems' fundamental lemma has recently received an impressive amount of attention in the (data-driven) control community. In this paper, we formulate a frequency-domain equivalent of this lemma. In doing so, we bridge the gap between…

Systems and Control · Electrical Eng. & Systems 2023-11-28 T. J. Meijer , S. A. N. Nouwens , V. S. Dolk , W. P. M. H. Heemels
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