A note on persistency of excitation

Willems, Jan C.; Rapisarda, Paolo; Markovsky, Ivan; Moor, Bart L.M. De

doi:10.1016/j.sysconle.2004.09.003

Cited by 606 publications

(266 citation statements)

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“…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. Assuming that ∆y is persistently exciting of sufficiently high order (Willems et al 2005), we have that the most powerful unfalsified model B mpum (∆y) of ∆y is the system ∆B. Since, by definition,…”

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

confidence: 99%

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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%

“…In the case of exact measurements, 2n + 1 data points are sufficient to identify the system exactly (Willems et al 2005). In the case of noisy data, the convergence rate of the parameters depends on the algorithm and the measurement process.…”

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confidence: 99%

An application of system identification in metrology

Markovsky

2015

Control Engineering Practice

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“…From Proposition 6 it follows that every column of the matrix F, computed on step 2 of Algorithm 2, is a free response of B. Moreover, from (Willems et al 2005, Corollary 2) and the assumption T r ≥ l(B) it follows that rank(F) = n(B). The statement of the proposition follows from rank(O) = rank(F) = n(B).…”

Section: Special Case U = 0: Zero Input Responsementioning

confidence: 91%

Data-driven simulation and control

Markovsky¹,

Rapisarda²

2008

International Journal of Control

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Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a system to a given input and initial conditions directly from a trajectory of the system, without explicitly identifying the system from the data. Similarly to the classical approach for simulation, the classical approach for control is model-based: first a model representation is derived from given data of the plant and then a control law is synthesised using the model and the control specifications. We present an approach for computing a linear quadratic tracking control signal that circumvents the identification step. The results are derived assuming exact data and the simulated response or control input is constructed off-line.

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“…In Corollary 2 of Willems, Rapisarda, Markovsky, and De Moor (2005), it has been shown that, for every trajectory (u, x) of a statespace system σ x = Ax + Bu with n-dimensional state vector x and m-dimensional input u, it holds that u p.e. of order n ⇒ rank…”

Section: Noise-free Identificationmentioning

confidence: 99%

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Rapisarda

Trentelman

2011

Automatica

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a b s t r a c tWe illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.

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A note on persistency of excitation

Cited by 606 publications

References 10 publications

An application of system identification in metrology

An application of system identification in metrology

Data-driven simulation and control

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

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