Identification Of A Class Of Wiener Nonlinear Systems (Ⅰ)

This thesis is based on the project "Study of Modelling and Identification of a Class of Nonlinear Systems (The National Nature Science Foundation of China 60574051)", and the thesis is a kind of basal research and have meaning both in theroy and applications. After reading plentiful references in the literature, the author researches Wiener nonlinear systems with white and colored noise deeply. And the convergence properties of some parameter estimation methods propesed are analyzed. The main contribution in the thesis are as follows.1. Some Wiener nonlinear output system models are introduced. To aim at the Wiener nonlinear models with white noise, the thesis proposes recursive least squares algorithm and stochastic gradient algorithm to estimates its parameters. Because the obtained nonlinear parameter estimates include the product terms of parameters of linear block and nonlinear block, average method, permutation and combination method and singular value decomposition method are proposed to separate the parameter estimates in this thesis. Finally, we compare these methods by a simulation example.2. Studing identification methods for Wiener nonlinear output systems, whose noise models are moving average modeIs(Wiener nonlinear ARMAX models). The difficulty in identification is that the information vector contains the noise which is not measurable. We can use residual value instead of that noise. So in this thesis, an iterative least squares algorithm, an extended recursive least squares algorithm and an extended recursive stochastic gradient algorithm are derived. The following digital examples illustrate the methods can achieve high precision.3. When the noise models are auto regressive models, we also call these systems Wiener nonlinear dynamic adjustment models. For these models, this thesis proposes an iterative generalized least squares algorithm, a generalized recursive least squares algorithm and a generalized recursive stochastic gradient algorithm. Because the stochastic gradient identification methods have slow convergence rate, we can introduce a forgetting factor A to improve its tracking performance. Finally, we test the algorithms proposed in this thesis by simulation examples and show their effectiveness.4. To aim at the Wiener nonlinear models with auto regressive moving average noise models, the thesis proposes an iterative extended generalized least squares algorithm, an extended generalized recursive least squares algorithm and an extended generalized recursive stochastic gradient algorithm. In order to improve the tracking performance of the stochastic gradient algorithm, a forgetting factor is also introduced. The simulation results shows those algorithms are effective.This thesis only deduces some identification algorithms for these kinds of systems and gives some simulation examples, but their convergence prove needs to study furtherly.