A note on persistency of excitation

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

doi:10.1109/cdc.2004.1428856

Cited by 193 publications

(536 citation statements)

References 10 publications

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“…The persistency of a signal is related to the rank of the regressor matrix (4). Roughly speaking, if the regressor matrix (4) has a moderate condition number for largen, then u(k) is highly persistent.…”

Section: A Sinusoidal Persistencymentioning

confidence: 99%

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Input richness and zero buffering in time-domain identification

Holzel

Ali

Bernstein

2010

Proceedings of the 2010 American Control Conference

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We consider the notion of persistency within a deterministic, finite-data context, namely, in terms of the rank and condition number of the regressor matrix, which contains input and output data. The novel contribution of this work is the technique of zero buffering, in which the input signal begins with a sequence of zeros. We show that the degree of persistency of the input, which is the order of the minimal AR model that can generate the input signal, is increased by zero buffering. We then demonstrate the effectiveness of zero buffering in increasing the degree of persistency of a Schroeder-phased signal, which, without zero buffering, yields a poorly conditioned regressor matrix. We also investigate the feasibility of estimating the dynamic order in terms of the singular values of the regressor matrix by showing that the rank of the regressor matrix is related to the degree of persistency of the input, the order of the model, and the order of the true system. Under reasonable signal to noise ratios, this technique provides a useful estimate of the true system order.

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Section: A Sinusoidal Persistencymentioning

confidence: 99%

“…In [2], signals that maximize persistency as defined by various cost criteria are examined, whereas in [3], persistency in the time domain is based on the informative value of the state. Persistency within a behavioral context is developed in [4].…”

Section: Introductionmentioning

confidence: 99%

Input richness and zero buffering in time-domain identification

Holzel

Ali

Bernstein

2010

Proceedings of the 2010 American Control Conference

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“…The results of [6] apply for finite time series but relay on the unverifiable from the data w d assumption (2). Based on the fundamental lemma, we give verifiable from the data conditions under which (2) holds.…”

Section: And Futurementioning

confidence: 92%

“…Under what conditions can this model be recovered back from the data? This identifiability question is answered in [2]. In order to state the result, we introduce notation for block-Hankel matrix constructed from a time series…”

Section: Introductionmentioning

confidence: 99%

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State Representations From Finite Time Series

Markovsky¹,

Willems²,

Moor³

Proceedings of the 44th IEEE Conference on Decision and Control

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We present two algorithms for construction of a state sequence of a linear time-invariant system from a finite exact trajectory of that system. The first algorithm uses the classical in subspace identification splitting of the data into "past" and "future" and computes a bases for the past-future intersection. The second algorithm, based on the shift-and-cut map, operates on a half deeper Hankel matrix.Index Terms-Subspace identification, state construction, shift-and-cut map, persistency of excitation, behavioral systems.

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Real‐time identification of nonlinear multiple‐input–multiple‐output systems with unknown input time delay using Wiener model with Neuro‐Laguerre structure

Sadeghi¹,

Farrokhi

2018

Adaptive Control & Signal

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In this article, a real-time block-oriented identification method for nonlinear multiple-input-multiple-output systems with input time delay is proposed. The proposed method uses the Wiener structure, which consists of a linear dynamic block (LDB) followed by a nonlinear static block (NSB). The LDB is described by the Laguerre filter lattice, whereas the NSB is characterized using the neural networks. Due to the online adaptation of the parameters, the proposed method can cope with the changes in the system parameters. Moreover, the convergence and bounded modeling error are shown using the Lyapunov direct method. Four practical case studies show the effectiveness of the proposed algorithm in the open-loop and closed-loop identification scenarios. The proposed method is compared with the recently published methods in the literature in terms of the modeling accuracy, parameter initialization, and required information from the system. How to cite this article: Sadeghi M, Farrokhi M. Real-time identification of nonlinear multiple-inputmultiple-output systems with unknown input time delay using Wiener model with Neuro-Laguerre structure. Int J Adapt Control Signal Process. 2019;33:157-174. https://doi.

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A note on persistency of excitation

Cited by 193 publications

References 10 publications

Input richness and zero buffering in time-domain identification

Input richness and zero buffering in time-domain identification

State Representations From Finite Time Series

Real‐time identification of nonlinear multiple‐input–multiple‐output systems with unknown input time delay using Wiener model with Neuro‐Laguerre structure

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