Related papers: Robust Fundamental Lemma for Data-driven Control
In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that…
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…
This paper presents a data-driven receding horizon control framework for discrete-time linear systems that guarantees robust performance in the presence of bounded disturbances. Unlike the majority of existing data-driven predictive control…
Predictive control, which is based on a model of the system to compute the applied input optimizing the future system behavior, is by now widely used. If the nominal models are not given or are very uncertain, data-driven model predictive…
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…
Given measurements of a linear time-invariant system, the McMillan degree is the dimension of the smallest such system that reproduces these observed dynamics. Using impulse response measurements where the system has been started in some…
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…
This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured…
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…
This letter presents a robust data-driven receding-horizon control framework for the discrete time linear quadratic regulator (LQR) with input constraints. Unlike existing data-driven approaches that design a controller from initial data…
This paper studies finite-horizon robust tracking control for discrete-time linear systems, based on input-output data. We leverage behavioral theory to represent system trajectories through a set of noiseless historical data, instead of…
This paper introduces a Data-Fused Model Predictive Control (DFMPC) framework that combines physics-based models with data-driven representations of unknown dynamics. Leveraging Willems' Fundamental Lemma and an artificial equilibrium…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
Willems' fundamental lemma uses a key decision variable $g$ to combine measured input-output data and describe trajectories of a linear time-invariant system. In this paper, we ask: what is a good choice for this vector $g$ when the system…
In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions…
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…
Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…
Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we…
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…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…