A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models

Salhi, Houda; Kamoun, S.

doi:10.1016/j.apm.2015.03.050

Cited by 56 publications

(23 citation statements)

References 38 publications

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“…Remark By using the following quadratic Lyapunov function:

V = \frac{1}{2} ((), {\overset{true˜}{boldx}}^{T} P_{1} \overset{x}{true} + {\overset{true˜}{bolda}}^{T} P_{2}^{- 1} \overset{a}{true} + tr ((), {\overset{true˜}{boldB}}^{T} P_{3}^{- 1} \overset{B}{true})),

which has been widely used in identification techniques, instead of Gaussian Lyapunov function , it can be easily seen that the identification laws would be

({, \begin{array}{l} D^{α} \overset{a}{true} = P_{2} e y^{f} \\ D^{α} \overset{B}{true} = - P_{3} e {\overset{true˜}{boldU}}^{T} . \end{array})

…”

Section: Identification Algorithmmentioning

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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“…Remark By using the following quadratic Lyapunov function:

V = \frac{1}{2} ((), {\overset{true˜}{boldx}}^{T} P_{1} \overset{x}{true} + {\overset{true˜}{bolda}}^{T} P_{2}^{- 1} \overset{a}{true} + tr ((), {\overset{true˜}{boldB}}^{T} P_{3}^{- 1} \overset{B}{true})),

which has been widely used in identification techniques, instead of Gaussian Lyapunov function , it can be easily seen that the identification laws would be

({, \begin{array}{l} D^{α} \overset{a}{true} = P_{2} e y^{f} \\ D^{α} \overset{B}{true} = - P_{3} e {\overset{true˜}{boldU}}^{T} . \end{array})

…”

Section: Identification Algorithmmentioning

confidence: 99%

“…which has been widely used in identification techniques, 11,15,27 instead of Gaussian Lyapunov function (21), it can be easily seen that the identification laws would be { Dâ = P 2 ey…”

Section: Identification Algorithmmentioning

confidence: 99%

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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“…13 Recently, a recursive parameter estimation algorithm has been developed for multi-input-single-output and multi-input-multi-output nonlinear systems. 14 As an important class of MIMO systems, the multivariate systems are often encountered in practice. 15,16 The multivariate systems are a kind of MIMO systems in which the subsystem parameter vectors are coupled and the subsystem information vectors are independent.…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

Liu

Ding

Hayat

2019

Adaptive Control & Signal

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For the multivariate equation-error moving average system, a multivariate maximum likelihood multi-innovation extended stochastic gradient (M-ML-MIESG) algorithm is delivered. The key is to decompose the system into several regressive identification subsystems according to the number of the system outputs. Then, a multivariate maximum likelihood extended stochastic gradient algorithm is presented to estimate the parameters of these subsystems. The M-ML-MIESG algorithm has higher parameter estimation accuracy than the multivariate extended stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.

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“…For example, Zhang and Hoagg used a candidate-pool approach to identify the feedback and feedforward transfer function matrices and presented a frequency-domain technique for identifying multivariable feedback and feedforward systems [8]; Salhi and Kamoun proposed a recursive algorithm to estimate the parameters of the dynamic linear part and the static nonlinear part of multivariable Hammerstein systems [9].…”

Section: Introductionmentioning

confidence: 99%

Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems

Huang

Ding

2017

Algorithms

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This paper focuses on the recursive identification problems for a multivariate output-error system. By decomposing the system into several subsystems and by forming a coupled relationship between the parameter estimation vectors of the subsystems, two coupled auxiliary model based recursive least squares (RLS) algorithms are presented. Moreover, in contrast to the auxiliary model based recursive least squares algorithm, the proposed algorithms provide a reference to improve the identification accuracy of the multivariate output-error system. The simulation results confirm the effectiveness of the proposed algorithms.

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A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models

Cited by 56 publications

References 38 publications

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems

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