Design of Asymptotically Convergent Frequency Estimator Using Contraction Theory

Sharma, Bharat Bhushan; Kar, Indra Narayan

doi:10.1109/tac.2008.927682

Cited by 41 publications

(24 citation statements)

References 24 publications

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“…The adaptive observer is another key methodology exploited to track multiple frequencies because of its notable feature in terms of stability: global or semi-global stability is ensured in most cases (see [23], [24], [25], [26], [27] and [28]). In particular, [26] presents a simplified global stability analysis by using contraction theory rather than traditional Lyapunov analysis; and, on the other hand, [28] proposes a hybrid observer to identify the n frequencies from a multi-frequency signal with saturated amplitudes.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, [26] presents a simplified global stability analysis by using contraction theory rather than traditional Lyapunov analysis; and, on the other hand, [28] proposes a hybrid observer to identify the n frequencies from a multi-frequency signal with saturated amplitudes. Recently, the effectiveness of the hybrid observer in the presence of poorly sampled signal is shown in [29].…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

Chen

et al. 2018

IEEE Trans. Automat. Contr.

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Abstract-This paper presents an adaptive observer-based robust estimation methodology of the amplitudes, frequencies and phases of biased multi-sinusoidal signals in presence of bounded perturbations on the measurement. The parameters of the sinusoidal components are estimated on-line and the update laws are individually controlled by an excitation-based switching logic enabling the update of a parameter only when the measured signal is sufficiently informative. This way doing, the algorithm is able to tackle the problem of over-parametrization (i.e., when the internal model accounts for a number of sinusoids that is larger than the true spectral content) or temporarily fading sinusoidal components. The stability analysis proves the existence of a tuning parameter set for which the estimator's dynamics are input-to-state stable with respect to bounded measurement disturbances. The performance of the proposed estimation approach is evaluated and compared with other existing tools by extensive simulation trials and real-time experiments.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

Chen

et al. 2018

IEEE Trans. Automat. Contr.

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“…Examples include intrinsic observer design [AR03], consensus problems in complex networks [WS05], output regulation of nonlinear systems [PvdWN05], design of frequency estimators [SK08b], synchronization of coupled identical dynamical systems [RdBS09], construction of symbolic models for nonlinear control systems [PGT08,PT09,GPT09], and the analysis of bio-molecular systems [RdB09]. Our motivation comes from symbolic control where incremental stability was identified as a key property enabling the construction of finite abstractions of nonlinear control systems [PGT08,PT09,GPT09,ZPJT10].…”

Section: Introductionmentioning

confidence: 99%

Backstepping Design for Incremental Stability

Zamani

Tabuada

2011

IEEE Trans. Automat. Contr.

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Abstract. Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this paper, we develop a backstepping design approach for incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a synchronous generator incrementally stable.

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“…Contraction theory is recently developed tool for analyzing the stability and synchronization of nonlinear control system. Some of important results of contraction theory can be found in literature [5][6][7][8][9][10] & references therein. In observer based synchronization approach, the actual system states are reconstructed by utilizing the information available at the actual system output.…”

Section: Introductionmentioning

confidence: 99%

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

Vaishnav¹

2012

IOSRJEEE

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Design of Asymptotically Convergent Frequency Estimator Using Contraction Theory

Cited by 41 publications

References 24 publications

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

Backstepping Design for Incremental Stability

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

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