The parameter estimation algorithms based on the dynamical response measurement data

IET Control Theory & Applications

et al. 2018

Self Cite

128

Abstract:In the revised paper, we have highlighted the changes made in Blue FONT. This paper presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on basis of the decomposition-coordination principle, a BSO based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms. IntroductionParameter estimation is a significant part in system identification, and has been widely used in system analysis [1][2][3], system modeling [4][5][6][7], and system control [8,9]. Since many industrial processes are complex and inherently nonlinear, nonlinear system identification has drawn much attention throughout the world [10][11][12]. The bilinear approach for modeling these complex processes are proven to be more precise than any other traditional linear models [13]. However, the nonlinear term existing in the bilinear model brings some challenges for bilinear system identification. During the past decades, much work has been carried out on parameter estimation for bilinear systems. For example, dos Santos et al. presented a subspace identification method for bilinear systems by treating the bilinear term as a second-order white noise process [14]. Larkowski et al. addressed the identification problem of the diagonal bilinear errors-in-variables system and extended the bias compensated least squares technique to bilinear systems [15]. Li et al. applied the polynomial transformation technique to obtain the equivalent input-output representation of the bilinear system and proposed the iterative algorithm for parameter estimation [16][17][18]. The recursive least squares (RLS) approach is known as the most commonly used estimation method among numerous different parameter estimation techniques. Although the RLS method offers a fast convergence rate, there exists several problems such as the increase in the computational burden and the decline in the tracking capability [19,20]. The hierarchical identification principle is applied to decompose a bilinear system into several subsystems Nonlinear filtering techniques have attracted much attention in signal processing [26,27] and have wide applications in many areas [28][29][30][31]. The classical Kalman filter (KF) is recognized as the best linear filter for linear systems under Gaussian noises. However, it is not suitable f...

Section: Discussionmentioning

confidence: 99%

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

Zhang

IET Control Theory & Applications

et al. 2018

Self Cite

128

“…Time delays often exist in signal transmission and signal modeling [12][13][14][15][16] and control systems. [17][18][19] For example, in communication, the measurements are often obtained with time delay because of the transmission congestion; the communication networks between subsystems are often unreliable, which will introduce the communication delays.…”

Section: Introductionmentioning

confidence: 99%

Highly computationally efficient state filter based on the delta operator

Xiao

Adaptive Control & Signal

et al. 2019

Self Cite

161

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

“…System identification and parameter estimation methods have been used to model some dynamical systems [1][2][3][4] and signal models, 5,6 including some nonlinear systems. [7][8][9] Multiple-input-multiple-output (MIMO) systems are common in practical industrial processes because of complex structures and high dimensions.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Adaptive Control & Signal

Hayat

2019

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.