Abstract
Nonlinear system identification is considered, where the nonlinear static function was approximated by a number of polynomial functions. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The identification procedure is divided into two steps. Firstly we adopt the extended stochastic gradient algorithm to identify some unknown parameters. Secondly using singular value decomposition (SVD), we propose a new method to identify other parameters. The basic idea is to replace un-measurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. The applicability of the approach is illustrated by a simulation.
Highlights
Modeling, identification and prediction are three main ubiquitous phenomena in our daily lives
An ideal model should be simple, accurate and general. This approximate description of the system can be constructed by system identification strategy, as the goal of system identification is to build a mathematical model of a dynamic system based on some initial information about the system and the measurement data collected from the system
System identification is an iterative process and if the quality of the obtained model is not satisfactory, some or all of the listed phases can be repeated in order to obtain one satisfied model
Summary
Identification and prediction are three main ubiquitous phenomena in our daily lives. An ideal model should be simple, accurate and general This approximate description of the system can be constructed by system identification strategy, as the goal of system identification is to build a mathematical model of a dynamic system based on some initial information about the system and the measurement data collected from the system. System identification is an iterative process and if the quality of the obtained model is not satisfactory, some or all of the listed phases can be repeated in order to obtain one satisfied model. Reference [5] considered an extended stochastic gradient identification algorithm for Hammerstein-Wiener ARMAX systems. Reference [7] considered two identification algorithms, an iterative gradient and a recursive stochastic gradient based, for a Hammerstein nonlinear ARMAX model
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