Identification Methods For Bilinear State Space System

Most of the practical processes show nonlinear characteristics to some extent.Using linear models to describe the dynamic characteristics of the systems may not obtain satisfactory results.It has been an inevitable trend to study the identification methods for nonlinear systems.As a typical class of nonlinear system,the bilinear system is linear with respect to state and control respectively,but not at the same time,and has an obvious changeable structure,which makes it show good control performance in describing some nonlinear industrial plants.This thesis discuss the problem of parameter identification for the bilinear state space system.The mainly research works are as follows:(1)Aiming at the problem of that the traditional gradient iterative(GI)algorithm needs to collect a batch of data in advance for offline identification,a dynamic sliding window is designed to update the training data by combining the ideas of the recursive and iterative algorithms.Within each set of data window in SW-GI algorithm,the GI algorithm is first used to obtain parameter estimates by processing the training data,and then as the data window moving,the new measured data is applied to further update the parameter estimates.For the unknown state variables in the model,a bilinear state observer is adopted to calculate their estimates.Then,by means of the interactive estimation theory,the sliding window gradient iterative algorithm based on state observer is derived to obtain the joint estimates of parameter and state for bilinear model.The numerical simulation shows the effectiveness of the algorithm.(2)Obtaining the reliable range of parameters is the key to design the controller for system,while the current point estimation algorithm can not evaluate the reliability of parameters.Therefore,by introducing the probability distribution to describe the uncertainty of parameters,the problem of parameter distribution estimation for bilinear model has been studied under the framework of variational Bayesian(VB)algorithm.The unknown parameters of bilinear system are regarded as random variables in this method.And by giving the corresponding prior distributions,the optimal approximate solution for the parameters posterior distribution is obtained by maximizing the lower bound of the marginal likelihood function of the measurement data.Moreover,the Kalman Filter with time-variant gain is proposed to estimate the states of bilinear system.Then,the Kalman Filter based variational Bayesian iterative algorithm is derived to compare with the observer based identification algorithm.The simulation results verify that the proposed method can effectively improve the estimation accuracy of parameters.(3)The variational Bayesian identification problem for bilinear state space models with Markov-switching time delays is studied.Aiming at the problem of uncertain time delays,the Markov chain is adopted to model the correlation between time delays.The unknown time delays are regarded as hidden variables in the VB algorithm,and the free distribution is introduced to approximate the true posterior distribution of parameter and time delay.The VB method transforms the problem of minimizing the distance between the free distribution and the true posterior distribution into maximizing the lower bound of the marginal likelihood of measurement data,and obtains the approximate posterior distributions of parameter and delay by iteratively maximizing the lower bound function.Then,by combining the proposed Kalman Filter with time-variant gain,the joint estimation of the model parameters,the delays,the transition parameters of Markov chain and the states is obtained.The results of numerical simulation and continuous stirred tank reactor simulation demonstrate the effectiveness of the algorithm.