Nonlinear System Identification With Robust Multiple Model Approach

Liu, Xin; Yang, Xianqiang; Yin, Shen

doi:10.1109/tcst.2019.2947868

Cited by 11 publications

(5 citation statements)

References 31 publications

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“…3. Form the information vector 𝝋( b(k − 1), k) by (18). Compute the gain vector L(k) and the covariance matrix P(k) by ( 16) and ( 17).…”

Section: The Overall Recursive Least Squares Algorithmmentioning

confidence: 99%

“…Recently, Zhang et al investigated the iterative identification approach for the nonlinear time‐delay systems by utilizing the observation data 17 . Liu et al solved the parameter estimation problem by the expectation maximization algorithm for the nonlinear systems from the noisy output data 18 …”

Section: Introductionmentioning

confidence: 99%

“…17 Liu et al solved the parameter estimation problem by the expectation maximization algorithm for the nonlinear systems from the noisy output data. 18 Nonlinearity and feedback are the important characteristics of controlled systems. As a fundamental class of nonlinear systems, the feedback nonlinear systems consist of two parts, including the dynamic linear model in the forward channel and the static nonlinear model in the feedback channel.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Wei

Xiao

et al. 2022

Intl J Robust & Nonlinear

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This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation‐error systems). The bilinear‐in‐parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive least squares algorithm is developed to handle the difficulty of the bilinear‐in‐parameter. For the purpose of avoiding the heavy computational burden, an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate. Furthermore, the convergence analysis of the proposed algorithms are established by means of the stochastic process theory. The effectiveness of the proposed algorithms are illustrated by the simulation example.

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“…3. Form the information vector 𝝋( b(k − 1), k) by (18). Compute the gain vector L(k) and the covariance matrix P(k) by ( 16) and ( 17).…”

Section: The Overall Recursive Least Squares Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Wei

Xiao

et al. 2022

Intl J Robust & Nonlinear

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show abstract

“…In addition, the collected data often contain outliers due to some random factors, such as sensor failure, operation failure, or other unknown interference. 17,18 The traditional outlier treatment method is to detect the outliers directly, and then applies the data after eliminating the outliers to identify the unknown parameters. However, this may lead to information loss, which is not conducive to parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

Expectation‐maximization algorithm for bilinear state‐space models with time‐varying delays under non‐Gaussian noise

Wang

Xiong

2023

Adaptive Control & Signal

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SummaryIn this paper, the parameter identification of bilinear state‐space model (SSM) in the presence of random outliers and time‐varying delays is investigated. Under the basis of the observable canonical form of the bilinear model, the system output can be written as a regressive form, and a bilinear state observer is applied to estimate the unknown states. To eliminate the influence of outliers and time‐varying delays on parameter estimation, we employ the Student's distribution to deal with the measurement noise and use a first‐order Markov chain to model the delays. In the framework of expectation‐maximization (EM) algorithm, the unknown parameters, delays, noise variance, states and transition probability matrix can be estimated iteratively. A numerical simulation and a continuous stirred tank reactor (CSTR) process demonstrate that the proposed algorithm has good immunity against outliers and time‐varying delays and offers good estimation accuracy for the bilinear SSM.

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“…These methods identify the linear or nonlinear input-output model without involving the model's structure. On the other hand, references [8,15,27,29] derived the mathematical model of the system and then conducted the system parameter identification to reconstruct the unknown system behavior. From the perspective of control applications, precise system parameter identification could give higher control performance.…”

Section: Introductionmentioning

confidence: 99%

An Integral Method for Parameter Identification of a Nonlinear Robot subject to Quantization Error

Peng

Juang

2023

Preprint

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This paper focuses on the parameter identification of a class of nonlinear mechanical dynamic systems subject to feedback quantization errors.} A second-order integral method for the parameter identification of a nonlinear two-degrees-of-freedom robotic manipulator is studied. To obtain accurate parameter estimates, an optimal excitation trajectory subject to state constraints is proposed. The designated excitation trajectory is able to minimize estimation uncertainties, providing the controlled system trajectory reaches the desired optimal excitation trajectory. Moreover, for most of the nonlinear robotic systems, the output measurements are acquired from the encoders subject to apparent quantization error. Directly differentiating the position to estimate the velocity and acceleration trajectories is unrealistic and unsuitable due to the amplified quantization errors will cause considerable estimation errors. Instead, the finite Fourier series is introduced to perform optimal estimation of the position, velocity, and acceleration histories to capture the dominant frequencies of the system response. A weighted least-squares solution is further proposed to improve parameter identification precision. The comparative studies reveal that the integral method has superior parameter estimation performance than the direct difference model and the filtered regression model in the existing literature. Experimental simulations illustrate the effectiveness of the presented method.

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Nonlinear System Identification With Robust Multiple Model Approach

Cited by 11 publications

References 31 publications

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

Expectation‐maximization algorithm for bilinear state‐space models with time‐varying delays under non‐Gaussian noise

An Integral Method for Parameter Identification of a Nonlinear Robot subject to Quantization Error

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