Hierarchical recursive least squares parameter estimation of non-uniformly sampled Hammerstein nonlinear systems based on Kalman filter

Zhou, Lincheng; Li, Xiangli; Lei, Shan; Xia, Jingyan; Chen, Wei

doi:10.1016/j.jfranklin.2017.02.010

Cited by 17 publications

(11 citation statements)

References 28 publications

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“…The identification techniques mainly distinguish themselves in the way the static nonlinearity is represented and in the form of optimization problem that is finally obtained. Known approaches for different types of nonlinearities and estimation methods can be found eg in [1][2][3][4][5][6][7][8][9][10][11][12][13]. The Wiener model has a linear dynamic block followed by a nonlinear static block and many techniques have been proposed to solve the identification problems typically encountered in using this model, see, eg [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Identification of nonlinear block-oriented systems with backlash and saturation

Vörös

2019

Journal of Electrical Engineering

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A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

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Section: Introductionmentioning

confidence: 99%

Identification of nonlinear block-oriented systems with backlash and saturation

Vörös

2019

Journal of Electrical Engineering

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“…However, real systems are inherently continuous‐time and, as a result, continuous‐time modeling improves the identification performance . Besides, since the state‐space modeling provides a deep insight into the nature of the physical systems, it has been a subject of recent research . Some of the distinguishing features of the state‐space‐based identification over the commonly used input‐output regression‐based one are as follows: (i) by the use of state‐space realization of a system, the well‐known Lyapunov stability theory can be conducted to achieve stable identification laws, which ensure boundedness of the estimated parameters; (ii) state‐space modeling eliminates the need for filtering techniques such as those used in the works of Wu and Chen and Cui et al arises in the continuous‐time identification, provided that the system states are available.…”

Section: Introductionmentioning

confidence: 99%

“…In this situation, which is the case considered in this paper, the state‐space identification becomes difficult because it includes the estimation of not only the unknown parameters but also the unknown states. It is noteworthy that two main strategies have been presented in the literature on Hammerstein state‐space identification: (i) identification algorithms that are under the assumption of the system states being known and (ii) hierarchical methods based on the cost function minimization problem, which commonly bring the system back to its discrete‐time input‐output representation . Recently, the authors proposed an observer‐based state‐space identification using an auxiliary model‐based observer .…”

Section: Introductionmentioning

confidence: 99%

“…It is noteworthy that two main strategies have been presented in the literature on Hammerstein state-space identification: (i) identification algorithms that are under the assumption of the system states being known 15,16 and (ii) hierarchical methods based on the cost function minimization problem, which commonly bring the system back to its discrete-time input-output representation. 9,17 Recently, the authors proposed an observer-based state-space identification using an auxiliary model-based observer. 18 Although, in the authors' previous work, 18 joint state and parameter estimation is performed without the need for signal filtering techniques, the drawback of this method is its serious sensitivity to initial conditions.…”

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confidence: 99%

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Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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Summary This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.

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“…However, state estimation brings difficulty to the parameter estimation [29]. For linear Gaussian systems, the Kalman filter can achieve optimal estimation performance with a small amount of computational load, which is usually the preferred method of the state estimation for state-space models [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems

Fei

Guo

et al. 2019

Mathematics

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Many basic laws of physics or chemistry can be written in the form of differential equations. With the development of digital signals and computer technology, the research on discrete models has received more and more attention. The estimates of the unknown coefficients in the discretized difference equation can be obtained by optimizing certain criterion functions. In modern control theory, the state-space model transforms high-order differential equations into first-order differential equations by introducing intermediate state variables. In this paper, the parameter estimation problem for linear difference equation systems with uncertain noise is developed. By transforming system equations into state-space models and on the basis of the considered priors of the noise and parameters, a variational Bayesian iterative estimation algorithm is derived from the observation data to obtain the parameter estimates. The unknown states involved in the variational Bayesian algorithm are updated by the Kalman filter. A numerical simulation example is given to validate the effectiveness of the proposed algorithm.

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Hierarchical recursive least squares parameter estimation of non-uniformly sampled Hammerstein nonlinear systems based on Kalman filter

Cited by 17 publications

References 28 publications

Identification of nonlinear block-oriented systems with backlash and saturation

Identification of nonlinear block-oriented systems with backlash and saturation

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems

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