Performance analysis of the recursive parameter estimation algorithms for multivariable Box–Jenkins systems

Wang, Xuehai; Ding, Feng

doi:10.1016/j.jfranklin.2014.07.004

Cited by 33 publications

(11 citation statements)

References 41 publications

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“…The convergence of the recursive algorithms and the iterative algorithms can be proved by using the martingale convergence theorem or the stochastic process theory [17,34,35]. The following gives the convergence results of the MI-ESG algorithm and F-MISG algorithm through two theorems.…”

Section: The Convergence Resultsmentioning

confidence: 99%

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

Mao

Ding

2015

Digital Signal Processing

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Section: The Convergence Resultsmentioning

confidence: 99%

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

Mao

Ding

2015

Digital Signal Processing

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“…As a comparison, the following gives the auxiliary model based recursive least squares (AM-RLS) algorithm (Wang, Xu, & Ding, 2015) to demonstrate the superiority of the F-AM-RLS algorithm. For the MIMO system in (1) and (2), we define the parameter vector and information matrix as…”

Section: The Am-rls Algorithmmentioning

confidence: 99%

Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model

2016

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“…However, building the first principle models requires the complete knowledge of physical plants; thus, system identification has attracted much attention. System identification is to recognize the structure and parameters of the systems using available input-output data [19,20]. This paper focuses on the parameter identification problems of multivariate pseudo-linear regressive systems with colored noise.…”

Section: Introductionmentioning

confidence: 99%

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

Wang

Ding

2015

Adaptive Control & Signal

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The performance analysis of the recursive algorithms for the multivariate systems with an autoregressive moving average noise process is still open. This paper analyzes the convergence of two recursive identification algorithms, the multivariate recursive generalized extended least squares algorithm and the multivariate generalized extended stochastic gradient algorithm, for pseudo-linear multivariate systems and proves that the parameter estimation errors consistently converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithms work well. 825 distillation column [29]. In the system identification area, Saadatzi et al. used two-input two-output transfer-function matrix models to describe the dynamics of the electric wheelchair on an arbitrary slope, and proposed a pre-compensator to decompose the plant's dynamics and to improve the identification accuracy [30]. Gu et al. combined the recursive least squares algorithm with the state filtering to identify the canonical state space systems [31].In practical industrial processes, the observed output data are always corrupted by various noise. Some methods assume that noise is independent identically distributed or white. However, it may be more reasonable to adopt the colored noise or the correlated noise because noise is unmeasurable [32,33]. The regressive systems involving the colored noise or correlated noise are called the pseudo-linear regressive systems. Cerutti et al. used the autoregressive moving average (ARMA) model to represent the dynamics of brain potentials [34]. Zheng et al. proposed a biased compensation based recursive least squares method for stochastic linear systems with correlated noise [35].On the convergence of the identification algorithms, early researchers always assumed that the observation noise has zero mean, finite second-order moment, and higher-order moment [36]. Some recent studies relaxed these assumptions. Liu and Ding studied the convergence properties of the recursive least squares algorithm for multivariable stochastic systems [37]; Ding and Gu studied the convergence of the auxiliary model based stochastic gradient algorithm for output-error state-delay systems [38]; Ding presented a coupled least squares algorithm for the multivariable stochastic systems and analyzed its convergence [39]. To the best of the authors' knowledge, the performance analysis for the multivariable ARMA systems has not been fully investigated. The main contributions of this paper lie in the following.By utilizing the measurable input-output data, this paper presents a multivariate generalized extended stochastic gradient (M-GESG) algorithm and a multivariate recursive generalized extended least squares (M-RGELS) algorithm for estimating the parameters of multivariate pseudo-linear regressive systems. By using the stochastic martingale theory, this paper analyzes the convergence of the M-GESG algorithm and the M-RGELS algorithm for multivariate systems with ARMA noise process.Briefly, the remainder is...

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Performance analysis of the recursive parameter estimation algorithms for multivariable Box–Jenkins systems

Cited by 33 publications

References 41 publications

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

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