Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

Abstract

AbstractPiecewise‐linear nonlinearity is an effective representation for hard nonlinearities such as saturation, dead zone, and backlash, which can be also used as a general tool for approximating nonlinear characteristics. For the input piecewise‐linear output‐error autoregressive systems, we develop a parametric expression of the piecewise‐linear nonlinearity through a switching function and position functions, and derive the identification model of the system by using the key item separation. Based on the optimization criterion, an auxiliary model‐based multi‐innovation recursive generalized least‐squares algorithm is deduced for estimating the unknown parameters according to the obtained model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The filtering identification model of the system is derived and a filtering‐based multi‐innovation recursive generalized least‐squares algorithm is proposed. The simulation example demonstrates the effectiveness of the proposed algorithms and shows that the filtering‐based multi‐innovation recursive generalized least‐squares algorithm has better identification performance.