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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 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 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 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 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.