Iterative Identification Methods For Bilinear Systems Based On The Input-output Representation

Bilinear systems are a class of special nonlinear systems.They are jointly linear in the state and the force variable,and the bilinear models can describe some real processes.Therefore,it is of great theoretical significance and application prospect to study the identification methods of bilinear systems.In this thesis,we combine the auxiliary model identification idea,the hierarchical identification principle and the data filtering technique to develop the iterative methods for a class of bilinear state space systems based on the input-output representation.The main contributions of this thesis are summarized as follows.(1)The difficulty of identifying the bilinear state space systems is that their model structure includes the products of the states and inputs,the input-output representation of a bilinear state space system is derived for the identification through eliminating the state variables in the systems.Based on the introduced conditions of the noise,the obtained bilinear model can be classified into two generic groups: the output-error type model and the equation-error type model.(2)Using a filter to screen the input-output data of bilinear systems with colored noise can reduce the effect of the noise to the parameter estimation accuracy.A filtering based generalized gradient iterative algorithm is developed for bilinear systems with autoregressive noise.Furthermore,the proposed algorithm is extended to the parameter identification of the bilinear system with autoregressive moving average noise.(3)It is necessary to introduce an unknown intermediate variable for replacing the algebraic fraction contained in output-error type model.Therefore,an auxiliary model is constructed and its output is used to replace the unknown intermediate variable,and an auxiliary model based least squares iterative algorithm is proposed.Furthermore,based on the moving data window,an auxiliary model based multiinnovation least squares iterative algorithm is developed.(4)As the least squares based iterative methods involved with the computation of matrix inversion,the computation burden of the method is large when bilinear systems are high-dimensional systems.Therefore,based on the hierarchical identification principle,the identification model is divided into many low-dimensional sub-models for improving the computation efficiency.For the bilinear system with moving average noise,an auxiliary model based two-stage extended least squares iterative algorithm and an auxiliary model based three-stage extended least squares iterative algorithm are developed.(5)The maximum likelihood identification has excellent statistical properties.A maximum likelihood extended gradient based iterative algorithm and a maximum likelihood extended least squares based iterative algorithm are proposed for the bilinear systems with moving average noise.Furthermore,some maximum likelihood iterative methods are studied for the bilinear system with autoregressive moving average noise based on the hierarchical identification principle and the data filtering technique.This thesis verifies the effectiveness of each algorithm by giving numerical simulation examples,and compares and analyzes different parameter identification methods.