Data-driven simulation and control

Markovsky, Ivan; Rapisarda, Paolo

doi:10.1080/00207170801942170

Cited by 276 publications

(296 citation statements)

References 17 publications

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“…The main idea of the model-free methods (Favoreel 1999;Woodley 2001;Markovsky and Rapisarda 2008), pictorially shown in Figure 1, is to avoid the system identification step in classical model-based methods. The model-free method of (Markovsky 2015) is a subspace-type method (Van Overschee and De Moor 1996b) for solving the autonomous identification problem in Section 3.3, however, it estimates directly the parameter of interestū.…”

Section: Model-free Methods Of (Markovsky 2015)mentioning

confidence: 99%

An application of system identification in metrology

Markovsky

2015

Control Engineering Practice

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Metrology is advancing by development of new measurement techniques and corresponding hardware. A given measurement technique, however, has fundamental speed and precision limitations. In order to overcome the hardware limitations, we develop signal processing methods based on the prior knowledge that the measurement process dynamics is linear time-invariant.Our approach is to model the measurement process as a step response of a dynamical system, where the input step level is the quantity of interest. The solution proposed is an algorithm that does real-time processing of the sensor's measurements. It is shown that when the measurement process dynamics is known, the input estimation problem is equivalent to state estimation. Otherwise, the input estimation problem can be solved as a system identification problem. The main underlying assumption is that the measured quantity is constant and the measurement process is a low-order linear time-invariant system. The methods are validated and compared on applications of temperature and weight measurement.

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Section: Model-free Methods Of (Markovsky 2015)mentioning

confidence: 99%

An application of system identification in metrology

Markovsky

2015

Control Engineering Practice

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“…The question occurs of solving the simulation problem directly from the data without identifying a model representation as a byproduct and using it in a model based solution. We call the direct problem data-driven simulation [15]. The data-driven simulation problem is a mosaic-Hankel structured low-rank approximation problem with fixed (exact) and missing data.…”

Section: Data-driven Simulation and Controlmentioning

confidence: 99%

“…The methods in the paper are compared with an alternative subspace-type method ddsim [19,15] in terms of the relative approximation error e h = h − h 2 h 2 .…”

Section: Data-driven Simulationmentioning

confidence: 99%

Structured Low-Rank Approximation with Missing Data

Markovsky¹,

Usevich²

2013

SIAM J. Matrix Anal. & Appl.

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We consider low-rank approximation of affinely structured matrices with missing elements. The method proposed is based on reformulation of the problem as inner and outer optimization. The inner minimization is a singular linear least-norm problem and admits an analytic solution. The outer problem is a nonlinear least squares problem and is solved by local optimization methods: minimization subject to quadratic equality constraints and unconstrained minimization with regularized cost function. The method is generalized to weighted low-rank approximation with missing values and is illustrated on approximate low-rank matrix completion, system identification, and data-driven simulation problems. An extended version of the paper is a literate program, implementing the method and reproducing the presented results.

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“…Like most control problems dissipativity theory requires system models (state space, high order differential/difference equations); consequently, when such models are not available it is mandatory to perform system identification before studying dissipative systems. In recent developments of data-based approaches to control (Shi and Skelton (2000); Safonov and Tsao (1997); Rapisarda (2016, 2017); Markovsky and Rapisarda (2008)), where the design of a controller is based on system data rather than models, which are in many real-life situations not available, (see Hou and Wang (2013) for a formal definition of data-driven control and a summary of approaches in the literature). It has become important to link the theory of dissipativity and system data.…”

Section: Introductionmentioning

confidence: 99%

On Lyapunov functions and data-driven dissipativity

2017

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Our contribution in this paper is twofold. In the first part, we study Lyapunov functions when a plant is interconnected with a dissipative stabilizing controller. In the second, we present results on data-driven approach to dissipative systems. In particular, we provide conditions under which an observed trajectory can be used to determine whether a system is dissipative with respect to a given supply rate. Our results are based on linear difference systems for which the use of quadratic difference forms play a central role for dissipativity and Lyapunov theory.

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Data-driven simulation and control

Cited by 276 publications

References 17 publications

An application of system identification in metrology

An application of system identification in metrology

Structured Low-Rank Approximation with Missing Data

On Lyapunov functions and data-driven dissipativity

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