Parameter Identification For Input Nonlinear Output-error Systems

In industrial process control,the nonlinear phenomena are very common in the real operating systems.The identification for the nonlinear systems has been a hot topic.The input nonlinear system which is consisted by a static nonlinear block followed by a linear dynamic subsystem has been widely used to describe the dynamic systems which have input nonlinearities.The thesis considers the problem of parameter estimation for the input nonlinear output-error systems.The major results of the thesis are as follows.1.For the saturation input nonlinear output-error moving average systems,by means of the key term separation and the data filtering,the data filtering based stochastic gradient algorithm and the data filtering based forgetting factor stochastic gradient algorithm are presented.Using the martingale convergence theorem,the thesis proves that when the input signal is persistently excited,the parameter estimates of the data filtering based stochastic gradient algorithm will converge to true values.Furthermore,the proposed data filtering based forgetting factor stochastic gradient algorithm is extended to identify the preload nonlinear output-error systems.2.Considering the input nonlinear output-error autoregressive systems,in which the static nonlinear block is described by a polynomial about the input signal with known basis.By using of the model decomposition,the model decomposition based least squares iterative algorithm is derived.Moreover,by means of the technique of data filtering,a data filtering based decomposition least squares iterative algorithm for the input nonlinear output-error systems with colored noise is presented.The numerical simulation demonstrates the effectiveness of the proposed algorithms.3.Considering the canonical input nonlinear state space systems with output time delay,by means of the the Kalman filtering,a least squares iterative algorithm and a recursive least squares algorithm are derived to identify the input nonlinear systems with known output time delay.By extending the information vector and parameter vector,a recursive extended least squares algorithm is presented to realize the combined estimation for the unknown parameters,system states and time delay.Two numerical simulation examples are applied to demonstrate the effectiveness of the proposed algorithms.4.For the input nonlinear state space systems,by using the over-parameterization method,the single-input single-output input nonlinear state space model is transformed into a multi-input single-output linear state space model.Under the frame-work of the expectation maximization(EM)method and the Kalman smoother,the parameter estimation algorithm for the input nonlinear state space model is derived.The strategies for choosing the initial value for the EM algorithm is discussed.A numerical simulation example and a multi-tank experiment are employed to verify the effectiveness of the proposed algorithm.5.By extending the single model structure to the multi-model,the identification problem for the multi-model based input nonlinear output-error parameter-varying systems is discussed.Taking the each local model as an input nonlinear output-error model under each local operation space.Assigning a normalized weighting function to each local model and identifying each local model at the pre-designed working points,the output of the global model can be determined by a weighted combination of the output of each local model.Under the framework of the variational Bayesian approach,a variational Bayesian estimation algorithm for input nonlinear output-error parameter varying systems is derived.The posterior distribution of the unknown parameters are presented.Two numerical simulations and an experiment carried out on a multi-tank are applied to demonstrate that the proposed algorithm can work effectively.