Hierarchical gradient‐ and least‐squares‐based iterative estimation algorithms for input‐nonlinear output‐error systems from measurement information by using the over‐parameterization

Abstract

This article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms.

An efficient conjugate gradient based Cholesky CMA‐ES estimation algorithm for nonlinear systems

“…The simulation results show that the proposed AM-CG Cholesky CMA algorithm is computationally efficient and can achieve highly accurate parameter estimates, so it has good application value. The proposed approaches in the article can combine some mathematical tools and identification methods [50][51][52][53][54][55][56][57] to study the parameter estimation issues of other linear stochastic systems and nonlinear stochastic systems with different structures and disturbance noises [58][59][60][61][62] and can be applied to literatures [63][64][65][66][67][68][69][70][71][72] such as paper-making systems, information processing, engineering systems and so on. [73][74][75][76][77][78] 78.…”

A coupled recursive least squares algorithm for multivariable systems and its computational amount analysis by using the coupling identification concept

“…Furthermore, the proposed method can be extended to study the parameter identification problems of other linear or nonlinear stochastic multivariable systems with colored noises [109][110][111][112][113][114][115] and can be applied to chemical process control systems. In the future work, the further investigation is to combine the identification algorithms proposed in this article with other methods, [116][117][118][119][120][121][122] such as the multi-innovation identification theory, to enhance their ability to track time-varying parameters and to improve the efficient data utilization. Furthermore, combining the coupling identification concept with other identification methods [123][124][125][126][127][128] such as the Bayesian approach, the maximum likelihood method and the Kalman filter technique to study more complex parameter identification problems is also an interesting research direction in the future.…”

Filtered generalized iterative parameter identification for equation‐error autoregressive models based on the filtering identification idea

“…The proposed parameter estimation algorithms in this article are based on the identification model in (14). Many identification methods are derived based on the identification models of the systems [33][34][35][36][37][38] and these methods can be used to estimate the parameters of other linear systems and nonlinear systems [39][40][41][42][43][44] and can be applied to other fields [45][46][47][48][49][50][51] such as chemical process control systems.…”