Iterative Identification For Bilinear-in-Parameter Systems

With the deepening of the research on nonlinear phenomena,the identification problem of the nonlinear models has become increasingly prominent.Bilinear-in-parameter systems contain bilinear terms which consist of two parameter vectors and an information matrix.As a special kind of nonlinear systems,the bilinear-in-parameter models combine the advantages of flexibility of nonlinear models and easy control of linear models to some extent.Therefore,the identification research of the bilinear-in-parameter systems has the theoretical and practical signification.The iterative identification method is a batch data processing method,which can make full use of observation information to improve the identification results.This dissertation has carried out systematic research on the parameter estimation problem of the bilinear-in-parameter systems by means of iterative identification methods.The major results are as follows.(1)For the bilinear-in-parameter systems,the identification difficulty lies in the bilinear relationship between the system input and parameters.Inspired by the overparameterization method,a over-parameterization model gradient-based iterative algorithms and a over-parameterization model least squares-based iterative algorithms are proposed under the uniqueness assumption.The proposed least squares-based iterative algorithm usually presents a heavy computational burden in the identification process.In order to improve this,the decomposition principle is introduced to separate the effect of the two sets of parameters,i.e.,the coefficients of the bilinear terms from the parameters of the colored noise.Then,a over-parameterization model decomposition least squaresbased iterative method to estimate the parameters is derived.In addition,the hierarchical principle is developed to divide the bilinear parameter vectors into different parameter sets.Then,the hierarchical principle based iterative identification algorithms are proposed,which avoids the redundant parameters estimation and reduces the computational calculation.(2)For the bilinear terms,this dissertation discusses a new method to separate the bilinear parameter vectors,expressing the system output as a linear combination of all unknown parameters without the product terms of the parameters.Based on this,a parameter separation gradient-based iterative algorithm and a parameter separation least squares-based iterative algorithm are presented.Since the bilinear-in-parameter output error systems contain the fractional structure,the unknown intermediate variables produced in the process of linearization system are identified by establishing an auxiliary model.Based on this,the proposed identification methods of bilinear-in-parameter equation error systems are extended to the bilinear-in-parameter output error systems.(3)Considering the bilinear-in-parameter systems with the colored noises,in order to improve the parameter estimation accuracy,a decomposition hierarchical gradientbased iterative algorithm and a decomposition hierarchical least squares-based iterative algorithm are derived by means of the data filter.Furthermore,under the condition that the probability density function of the system output is known,a likelihood function is constructed by taking the parameter vectors to be estimated as independent variables.By maximizing the logarithmic likelihood function,a maximum likelihood gradient-based iterative identification algorithms and a maximum likelihood lease squares-based iterative identification algorithms are derived.(4)Considering the bilinear-in-parameter equation error systems with the dual-rate sampling,which have the missing outputs,the traditional iterative algorithms cannot directly identify the dual-rate systems.To address this,the parameter separation identification model is derived based on the dual-rate data.The particle filter is introduced that combines the kernel density estimation method to recover the missing measurements from the available observations.Then,a parameter separation particle filter gradient-based iterative identification method and a parameter separation particle filter least squares-based iterative identification method are proposed to realize the combined estimation for the unknown outputs and system parameters.To sum up,this dissertation first discusses the identification problem of the bilinearin-parameter equation error systems.From the perspective of linearizing the bilinear terms,the corresponding iterative methods are proposed based on the over-parameterization identification model,the hierarchical identification model,and the parameter separation identification model.Combined with the auxiliary model identification idea and particle filter,the proposed identification methods are extended to the bilinear-in-parameter output error systems and dual-rate bilinear-in-parameter equation error systems.