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This paper focuses on iterative parameter estimation methods for a nonlinear closed-loop system (i.e., a nonlinear feedback system) with an equation-error model for the open-loop part. By applying negative gradient search, a gradient-based iterative algorithm is constructed. To reduce the computational costs and improve the parameter estimation accuracy, the hierarchical identification principle is employed to derive a hierarchical gradient-based iterative algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problems of photovoltaic cell models. In order to overcome the complexity of the model structure, through applying the hierarchical identification principle and decomposing the photovoltaic cell model into two sub-models with a smaller number of parameters. The nonlinear identification model becomes a combination of a linear sub-model and a nonlinear sub-model. A two-stage gradient-based iterative and a two-stage Newton iterative algorithms are proposed to estimate the parameters of photovoltaic cell models by using the negative gradient search and the Newton method. The performance of the proposed algorithms is assessed by using the simulation from the experimental data, and the evaluation results test the effectiveness of the proposed algorithms. In particular, the model built by using the obtained parameter estimates can fit the I-V curve, the P-V curve and the maximum power point well. [ABSTRACT FROM AUTHOR]

This paper focuses on development of a three-stage iterative identification algorithm for parameter estimation of a Wiener model with autoregressive moving average (ARMA) noise entering between linear and nonlinear part. The proposed three-stage algorithm is developed based on generalized extended gradient iterative (GEGI) algorithm to increase the convergence rate at a low number of iterations. To increase the convergence rate, a second algorithm is derived based on generalized extended least squares algorithm (GELSI). The proposed 3-stage generalized extended least square iterative (3S-GELSI) algorithm will also decrease the computational burden compared to the single-stage algorithm. Finally, to show that the discussed methods can identify the considered system effectively, simulation results of three examples are provided. The results demonstrate that the 3-stage GEGI (3S-GEGI) algorithm outperforms its basic single-stage counterpart in terms of convergence rate. Moreover, the proposed 3S-GELSI algorithm exhibits even greater superiority in terms of convergence rate compared to other existing methods. Additionally, it will be demonstrated that the computational burden decreases in the 3S-GELSI algorithm, as indicated by the reduced number of total flops. • Identification of output nonlinear-Box Jenkins Wiener models with colored noise. • 3-stage algorithm is developed based on GEGI algorithm. • To increase the convergence rate, an algorithm is derived based on GELSI algorithm. • 3S-GELSI algorithm decrease the computational burden compared to the single-stage algorithm. • The unmeasurable signals and the unknown system parameters are estimated effectively. [ABSTRACT FROM AUTHOR]

This paper focuses on the identification problem for a class of bilinear-in-parameter systems with an additive noise modeled by an autoregressive moving average process. By using the over-parameterization model, the special form of the bilinear term can be obtained by the model equivalent transformation. Then, we use a decomposition of the model into two synthetic models in order to separate the effect of the two sets of parameters, i.e., the coefficients of the nonlinear basis functions from the parameters of the colored noise. Moreover, two decomposition based iterative algorithms are proposed to identify the unknown parameters. A numerical example is presented to confirm the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper presents an iterative method for the un-biased identification of linearMultiple-InputMultiple-Output (MIMO) discrete two-dimensional (2D) systems. The system discussed here has Auto-Regressive Moving-Average model with exogenous inputs (ARMAX model). The proposed algorithm functions on the basis of the traditional Iterative Generalized Least Squares (IGLS) method. In summary, this paper proposes a two-dimensional Multiple-Input Multiple-Output Iterative Generalized Least Squares (2DMIGLS) algorithm to estimate the unknown parameters of the ARMAX model. Finally, simulation results show the efficiency and accuracy of the presented algorithm in estimating the unknown parameters of the model in the presence of colored noise. [ABSTRACT FROM AUTHOR]

Maximum likelihood methods are based on the probability and statistics theory, and significant for parameter estimation and system modeling. This paper combines the maximum likelihood principle with the data filtering technique for parameter estimation of a class of bilinear systems. The input-output representation of a bilinear system is derived through eliminating the state variables in the model. Then, a filtering based maximum likelihood iterative least squares algorithm is proposed for identifying the parameters of bilinear systems with colored noises by filtering the input-output data with a filter. A least squares based iterative algorithm is given for comparison. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems. The filtering based maximum likelihood iterative least squares algorithm is more accurate under different noise variance, and has higher computational efficiency. [ABSTRACT FROM AUTHOR]

This paper investigates the identification methods for controlled autoregressive systems with autoregressive noise (i.e., equation-error autoregressive systems) from given input and output data. By applying the iterative technique and the hierarchical identification principle, an iterative least squares identification algorithm is presented and a recursive generalized least squares algorithm is given for comparison. The basic idea is to replace the unknown noise terms in the information vector with their estimated residuals. The simulation test results show the effectiveness of these algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification problem for multivariable equation-error systems with autoregressive moving average noise using the hierarchical identification principle and the multi-innovation identification theory. We propose a hierarchical gradient-based iterative (HGI) identification algorithm and give a gradient-based iterative (GI) identification algorithm for comparison. Meanwhile, the multi-innovation theory is used to derive the hierarchical multi-innovation gradient-based iterative (HMIGI) identification algorithm. The analysis shows that the HGI algorithm has smaller computational burden and can give more accurate parameter estimates than the GI algorithm and the HMIGI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper combines the maximum likelihood principle with the data filtering technique for parameter estimation of bilinear systems with autoregressive moving average noise. We give the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model, we use an estimated noise transfer function to filter the input-output data and derive a filtering-based maximum likelihood gradient iterative algorithm for identifying the parameters of bilinear systems with colored noises. A gradient-based iterative algorithm is given for comparison. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems. [ABSTRACT FROM AUTHOR]

This paper considers the parameter identification problem of bilinear systems, which are a special class of nonlinear systems. The basic idea is giving the input-output representation of the bilinear system through eliminating the state variables in the system. By using the hierarchical identification principle and the data filtering technique, we derive a gradient-based iterative (GI) algorithm, a hierarchical GI algorithm and a filtering-based GI algorithm for identifying the parameters of bilinear systems with colored noises. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems. [ABSTRACT FROM AUTHOR]

For a multivariable controlled autoregressive system with autoregressive noises, its corresponding identification model contains a parameter matrix and a parameter vector. This paper presents the hierarchical gradient-based iterative (HGI) algorithm to interactively estimate the parameter matrix and the parameter vector by using the hierarchical identification principle and the gradient search. The simulation results show that the HGI algorithm is effective. [ABSTRACT FROM AUTHOR]

Delay time that affects the performances of many control synthesis techniques in controlled systems is common in most chemical industries. Estimating the delay time is also a difficult problem in identification fields. In this paper, aiming at continuous processes with delay time, an iterative least square identification method is proposed in the frequency domain. By introducing a truncated first-order Taylor expansion, the delay time term is linearized. Linear regression equation for least squares (LS) is directly derived from the transfer function whose nonlinear term is replaced by a linear one. For reducing the linear approximation error and getting more accurate estimations of the model parameters, an iterative algorithm is developed based on the LS. Moreover, the proposed method can be easily extended to a closed-loop system without increasing the order of the identified model. Simulations verify the effectiveness, fast convergence rates, and robustness of the proposed identification algorithm. [ABSTRACT FROM AUTHOR]

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well. [ABSTRACT FROM AUTHOR]

This paper discusses the parameter estimation problems of multi-input output-error autoregressive (OEAR) systems. By combining the auxiliary model identification idea and the data filtering technique, a data filtering based recursive generalized least squares (F-RGLS) identification algorithm and a data filtering based iterative least squares (F-LSI) identification algorithm are derived. Compared with the F-RGLS algorithm, the proposed F-LSI algorithm is more effective and can generate more accurate parameter estimates. The simulation results confirm this conclusion. [ABSTRACT FROM AUTHOR]

This paper focuses on the parameter estimation problems of input nonlinear output error autoregressive systems. Based on the key variables separation technique and the auxiliary model identification idea, the output of the system is expressed as a linear combination of all the system parameters, the unknown inner variables in the information vector are replaced with the outputs of the auxiliary model and a gradient based and a least squares based iterative identification algorithms are derived. Simulation example is provided to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper derives a Newton iterative algorithm for identifying a Hammerstein nonlinear FIR system with ARMA noise (i.e., Hammerstein nonlinear controlled autoregressive moving average system). This method decomposes a Hammerstein nonlinear system into two subsystems using the hierarchical identification principle, estimating the parameters of the system directly without using the over-parameterization method. The simulation results show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced for estimating the parameters of these two models. In order to further improve the accuracy of the parameter estimation, a multi-innovation hierarchical least-squares algorithm based on the data filtering theory proposed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The Wiener system is an important class of output nonlinear systems. This paper presents a Newton iterative parameter estimation algorithm for Wiener nonlinear systems. The simulation results show that the proposed algorithm is effective. The proposed algorithm can be combined with other iterative methods to identify other linear or nonlinear systems with colored noises. [Copyright &y& Elsevier]

The state-space models are derived for nonuniformly sampled data systems and the corresponding transfer function models are obtained. Since the information vector in the identification model contains unmeasurable true outputs, the conventional stochastic gradient algorithm cannot be applied. In order to overcome this difficulty, the gradient-based iterative identification algorithms are presented by replacing the unmeasurable variables with their iterative estimates at the previous step. The simulation results show that the proposed algorithm has high estimation accuracy compared with the auxiliary model-based stochastic gradient algorithm. [ABSTRACT FROM PUBLISHER]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]

The parameter estimation problem for the Hammerstein systems with asymmetric preload nonlinearity is considered in this paper. The nonlinearity is described by the piecewise function, which brings difficulty to the identification. By introducing a switching function, the static nonlinearity is described by an expression with unknown preload points and slopes. By using the key term separation technique, the unknown parameters from the nonlinear block and linear block are decoupled and collected in a parameter vector. Under the gradient iterative (GI) algorithm with finite measured data, the estimates of unknown parameters are obtained. Furthermore, combining the ideas of the recursive and iterative algorithms, a dynamic sliding window is designed. By updating the training data, the sliding window removes the oldest data and adds the newest sampled data to keep the length of the training data unchanged. The sliding window gradient-based iterative algorithm is proposed to estimate the unknown parameters. Moreover, compared with the stochastic gradient algorithm, the sliding window GI algorithm can improve the accuracy of parameter estimation and the utilization of the system data. The numerical simulation example is employed to validate the effectiveness of the proposed algorithms.

This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced for estimating the parameters of these two models. In order to further improve the accuracy of the parameter estimation, a multi-innovation hierarchical least-squares algorithm based on the data filtering theory proposed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.