A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Ding, Feng; Chen, Huibo; Xu, Ling; Dai, Jiyang; Li, Qishen; Hayat, Tasawar

doi:10.1016/j.jfranklin.2018.01.052

Cited by 151 publications

(74 citation statements)

References 46 publications

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“…The identification steps of the algorithm in (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), and (40) to compute θ s,k t and θ n,k t are listed as follows: (2) Collect the input-output data u t and y t and construct φ s t using (33). …”

Section: The Problem Formulationmentioning

confidence: 99%

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Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

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The identification problem of multivariable controlled autoregressive systems with measurement noise in the form of the moving average process is considered in this paper. The key is to filter the input-output data using the data filtering technique and to decompose the identification model into two subidentification models. By using the negative gradient search, an adaptive data filtering-based gradient iterative (F-GI) algorithm and an F-GI with finite measurement data are proposed for identifying the parameters of multivariable controlled autoregressive moving average systems. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

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Section: The Problem Formulationmentioning

confidence: 99%

“…Many gradient-based algorithms, including the stochastic gradient algorithms [32][33][34] and the gradient-based iterative algorithms, have been developed using the multi-innovation identification theory, the maximum likelihood estimation methods [35,36], the key-term separation principle [37,38], and the data filtering theory.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

Self Cite

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“…20,21 The key idea is to decompose the identification model into several subidentification models, such that the scale of the optimization problem becomes small. 22,23 In this aspect, decomposing the Hammerstein controlled autoregressive system into several subsystems, Ding et al derived a hierarchical LS algorithm for estimating all the unknown parameters 24 ; using the hierarchical identification principle, Zhang et al exploited an interactive algorithm to identify unmeasurable states and parameters of bilinear systems. 25 The innovation is the useful information, which can improve the parameter and state estimation accuracy.…”

Section: Introductionmentioning

confidence: 99%

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

Ding

Sheng

2019

Adaptive Control & Signal

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Modeling an exponential autoregressive (ExpAR) time series is the basis of solving the corresponding prediction and control problems. This paper investigates the hierarchical parameter estimation methods for the ExpAR model.By the hierarchical identification principle, the original nonlinear optimization problem is transformed into the combination of a linear and nonlinear optimization problem, and then, we derive a hierarchical least squares and stochastic gradient (LS-SG) algorithm. Given the difficulty of determining the step-size in the hierarchical LS-SG algorithm, an approach is proposed to obtain the optimal step-size. To improve the parameter estimation accuracy, the multi-innovation identification theory is employed to develop a hierarchical least squares and multi-innovation stochastic gradient algorithm for the ExpAR model. Two simulation examples are provided to test the effectiveness of the proposed algorithms.

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“…The considerable ability of capturing the complexity and nonlinearity of real‐life systems is due to the high flexibility of these models. The various identification methods with different nonlinear optimization algorithms for Hammerstein models have been proposed which include correlation theory, neural networks, orthogonal functions, polynomials, piecewise linear model, the overparameterization model–based methods, the iterative identification methods, the key term separation principle‐based identification methods, the hierarchical identification methods, the blind identification methods, and the maximum likelihood/expectation maximization estimation methods …”

Section: Introductionmentioning

confidence: 99%

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

Moghaddam

Mojallali

Teshnehlab

2018

Math Methods in App Sciences

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This paper presents a new multiple-input-single-output nonlinear system identification method based on Hammerstein model, which includes a fractional transfer function and a Modified Radial Basis Function Neural Network (MRBFNN) as linear dynamic part and static nonlinear subsystem, respectively. The size of Radial Basis Function Neural Network (RBFNN) grows with the number of inputs exponentially. As a novel idea, the MRBFNN is proposed, whose adjustable parameters are far fewer than other RBFNNs presented yet. A Modified Genetic Algorithm is used to identify the fractional orders and the centers and widths of MRBFNN and obtain an initial estimation of other unknown parameters. The Recursive Least Square (RLS) method is used to improve the estimation by updating the weighting parameters of MRBFNN and the transfer function coefficients. The convergence analysis of the proposed RLS is provided. Simulation results show the effectiveness and accuracy of the proposed method. KEYWORDS fractional order, genetic algorithm, Hammerstein model, modified radial basis function, nonlinear system identification 6252

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A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Cited by 151 publications

References 46 publications

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

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