Willems’ fundamental lemma based on second-order moments

Ferizbegovic, Mina; Hjalmarsson, Håkan; Mattsson, Per; Schön, Thomas B.

doi:10.1109/cdc45484.2021.9683632

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…We note that behavioral theory has been popularized before in the context of data-driven control. Based on Willems' fundamental lemma [19] and its various extensions [20]- [23], a number of control problems were solved, such as output matching [24] and predictive control [25]- [28]. The control design typically involves the computation of (openloop) sequences of control inputs that live in the image of data Hankel matrices.…”

Section: Related Workmentioning

confidence: 99%

A behavioral approach to data-driven control with noisy input-output data

Waarde¹,

Eising²,

Camlibel³

et al. 2022

Preprint

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This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of inputoutput AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

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Section: Related Workmentioning

confidence: 99%

A behavioral approach to data-driven control with noisy input-output data

Waarde¹,

Eising²,

Camlibel³

et al. 2022

Preprint

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“…Originally developed in a behavioral context, the fundamental lemma is also instrumental for direct output matching control [16] and control by interconnection [34]. The result has been extended in various ways to different model classes and data setups [35], [36], [37], [38], [39], [40], [41], [42], [43]. Although initially developed for linear systems, the fundamental lemma has been applied in the context of the data-driven control of nonlinear dynamics, such as polynomial and Luré systems [44], [45], [46], [47], [48], [49].…”

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confidence: 99%

“…Downloaded on December 12,2023 at 10:13:52 UTC from IEEE Xplore. Restrictions apply.DECEMBER 2023 « IEEE CONTROL SYSTEMS37…”

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confidence: 99%

The Informativity Approach: To Data-Driven Analysis and Control

Van Waarde,

Eising,

Camlibel

et al. 2023

IEEE Control Syst.

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Roughly speaking, systems and control theory deals with the problem of making a concrete physical system behave according to certain desired specifications. To achieve this desired behavior, the system can be interconnected with a physical device, called a controller. The problem of finding a mathematical description of such a controller is called the control design problem.To obtain a mathematical description of a controller for a to-be-controlled physical system, a possible first step is to obtain a mathematical model of the physical system. Such a mathematical model can take many forms. For example, the model could be in terms of ordinary or partial differential equations, difference equations, or transfer matrices.There are several ways to obtain a mathematical model for the physical system. The usual way is to apply the basic physical laws that are satisfied by the variables appearing in the system. This method is called first principles modeling. For example, for electromechanical systems, the set of basic physical laws that govern the behavior of the variables in the system (conservation laws, Newton's laws, and Kirchoff's laws) form a mathematical model.An alternative way to obtain a model is to do experiments on the physical system: certain external variables in the physical system are set to take particular values, while, at the same time, other variables are measured. In this way, one obtains data on the system that can be used to find mathematical descriptions of laws that are obeyed by the system variables, thus obtaining a model. This method is called system identification.The second step in a control system design problem is to decide which desired behavior we would like the physical system to have. Very often, this desired behavior can be formalized by requiring the mathematical model to have certain qualitative or quantitative mathematical properties. Together, these properties form the design objective.

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