Auxiliary model‐based iterative parameter estimation for a nonlinear output‐error system with saturation and dead‐zone nonlinearity

Abstract

This article is concerned with the parameter estimation problem of a nonlinear output‐error system with saturation and dead‐zone nonlinearity. The saturation nonlinearities and the dead‐zone nonlinearities are widely encountered in engineering applications and the identification for the nonlinear systems with these nonlinearities is very crucial. Based on the over‐parameterization identification model and the auxiliary model identification idea, an auxiliary model least‐squares‐based iterative algorithm is presented for estimating the parameters of the nonlinear system with saturation and dead‐zone nonlinearity. In order to enhance the computational efficiency, an auxiliary model gradient‐based iterative algorithm is presented for the nonlinear system. Using the multi‐innovation identification theory, an auxiliary model multi‐innovation gradient‐based iterative algorithm is derived for tracking time‐varying parameters. An example is carried out to show the effectiveness of the proposed algorithms. The numerical simulation results show that all the proposed algorithms can generate accurate parameter estimates.

Hierarchical iterative identification algorithms for a nonlinear system with dead‐zone and saturation nonlinearity based on the auxiliary model

“…6. Compute the output xl (t) of the auxiliary model by (26), t = 1, 2, … , L, compute the parameter estimates m1,l and m2,l by ( 32) and ( 33), form the parameter estimation vector θl using (34). 7.…”

“…However, the over-parameterization identification method requires estimating the redundant parameters in the model, which leads to heavy computational loads. 26 In order to enhance the computational efficiency, the hierarchical identification principle is introduced to identify such nonlinear systems. The hierarchical identification principle is to estimate the parameters of a system separately by transforming the system into several fictitious subsystems.…”

Fractional Gradient Descent-Based Auxiliary Model Algorithm for FIR Models with Missing Data

“…Owing to the network congestion, some data of the dynamic systems are missing [27][28][29]. Usually, two standard tools are applied to systems with missing data: (1) the lifting technique, e.g., the polynomial transformation algorithm [30], whose key is to transform the system into a lifted system with high order and then estimate the parameters based on all the measurable data; (2) the imputation technique, e.g., the auxiliary model method [31], frst estimates the missing data and then updates the parameters based on the measurable data and estimated data. Since the lifting method can enlarge the number of unknown parameters, this study focuses on the imputation method.…”

Deterministic and Stochastic Modeling Approaches for Saturation Nonlinearity

“…Nonlinearities in systems can be roughly divided into two categories: the polynomial nonlinearity and the hard nonlinearity [2,5]. Compared with the polynomial nonlinearity, the hard nonlinearity cannot be written as the analytic expression of the input and is more widely encountered in engineering practice [6].…”