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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]

Saturation nonlinearity exists widely in various practical control systems. Modeling and parameter estimation of systems with saturation nonlinearity are of great importance for analyzing their characteristics and controller design. This paper focuses on the identification issue of the input nonlinear Box–Jenkins systems with saturation nonlinearity. The input saturation nonlinearity is presented as a linear parametric expression through the application of a switching function, then the identification model of the system is derived by using the key term separation technique. Based on this model and the data filtering technique, the filtering identification model of the system is given by changing the system structure without changing the relationship between the input and output, which can reduce the interference of the colored noise and improve the identification accuracy. Then a data filtering-based maximum likelihood gradient-based iterative algorithm is proposed to estimate the unknown parameters. The maximum likelihood gradient-based iterative algorithm is provided for comparison. The feasibility and superiority of the proposed approach are emphasized by a simulation example. [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]

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]

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]

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 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]