A note on state and parameter estimation in a van der Pol oscillator

Besançon, Gildas; Voda, Alina; Jouffroy, Guillaume

doi:10.1016/j.automatica.2010.06.033

Cited by 20 publications

(6 citation statements)

References 7 publications

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“…In [3], it was shown that a (forced) Liénard system with functions F 0 , G 0 linearly parametrized with respect to some parameter vector θ, in fact can take the following structure:…”

Section: A Observer Toolsmentioning

confidence: 99%

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Liénard type model of fluid flow in pipelines: Application to estimation

Torres

Besançon

Verde

2015

2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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This paper highlights how fluid flow in a pipeline can be represented as a nonlinear model of so-called Liénard type. It is then shown how the structure of this model is suitable for the design of algorithms to identify parameters of a pipeline or estimate unmeasurable states. This approach is illustrated by simulation results, for instance showing how to estimate the Darcy-Weisbach friction coefficient or the fluid acceleration.

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“…In [3], it was shown that a (forced) Liénard system with functions F 0 , G 0 linearly parametrized with respect to some parameter vector θ, in fact can take the following structure:…”

Section: A Observer Toolsmentioning

confidence: 99%

“…This will be done on the basis of former Liénard-based studies as in [3] on the one hand, and the observer design proposed in [2] on the other hand.…”

Section: Estimationmentioning

confidence: 99%

Liénard type model of fluid flow in pipelines: Application to estimation

Torres

Besançon

Verde

2015

2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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“…The nonlinear van der Pol oscillator is one of an important model for the phenomena of limit-cycle oscillation [29], [30]. The van der Pol oscillator with the presence of noises is modeled by the following differential equation…”

Section: A Van Der Pol Oscillatormentioning

confidence: 99%

A Discrete-Time State Estimation for Nonlinear Systems With Noises

Nguyen-Van

2020

IEEE Access

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This paper proposes a discrete-time observer to estimate states of continuous-time nonlinear systems with presences of noises. Most conventional discrete-time state observers are designed using discrete-time models, which are derived by applying the forward-difference method to continuous-time models without considering their poor accuracy. This poor accuracy of the discretization may affect the accuracy of the observer-based on it and lead to a misevaluation. The proposed observer is based on an application of the extended Kalman filter (EKF) for a discrete-time model derived by a discretization method called continualized discretization. The proposed observer was applied to estimate the states of the Lorenz and van der Pol oscillators, which have complex dynamics such as limit cycle and chaos. The simulation results showed that the proposed observer gives better performances in estimating the real state and retaining the system dynamics of the original continuous-time model than the conventional method.

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“…The Van der Pol oscillator is a significant nonlinear oscillator and has a wide spread use [13] [15]. Estimation of the friction coefficient along with the states of the oscillator is considered here as a test problem…”

Section: Case Studymentioning

confidence: 99%

Adaptive divided difference filter for nonlinear systems with unknown noise

Dey

Sadhu

Ghoshal

2014

Proceedings of the 2014 International Conference on Control, Instrumentation, Energy and Communication (CIEC)

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An Adaptive Divided Difference filter has been proposed for joint estimation of parameter and states of nonlinear systems in situations with unknown process noise statistics. The proposed filter, which is based on the innovation sequence, ensures improved estimation performance adapting the unknown process noise covariance. The performance of the filter is assessed with a benchmark nonlinear problem. Simulation results demonstrate that the performance of the proposed filter is superior compared to a non adaptive Divided Difference filter when the process noise covariance is unknown.

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A note on state and parameter estimation in a van der Pol oscillator

Cited by 20 publications

References 7 publications

Liénard type model of fluid flow in pipelines: Application to estimation

Liénard type model of fluid flow in pipelines: Application to estimation

A Discrete-Time State Estimation for Nonlinear Systems With Noises

Adaptive divided difference filter for nonlinear systems with unknown noise

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