Identification Methods And Performance Analyses For Multivariable Systems

System identifcation and parameter estimation are important for model-based control problems. Mostof the practical control plants are multivariable systems, with complex structures and uncertain distur-bances. Therefore, the study of identifcation methods and their convergence properties for multivariablesystems is of universal signifcance and has wide application prospects. In recent years, research of theidentifcation methods for multivariable systems has received much attention and a number of achievementshave been made. However, it is not mature enough compared with the identifcation methods for scalarsystems. Especially when the number of variables is large, the identifcation models are of high dimensions,resulting in signifcant computational costs in the identifcation algorithms. By using the coupled identi-fcation concept, the data fltering technique and the hierarchical identifcation principle, this dissertationaims to develop more efcient identifcation methods for multivariable systems and to study their conver-gence properties, which is important to enrich the system identifcation theory. The main contributionsare summarized as follows.1. The convergence properties of the recursive least squares (RLS) method and the stochastic gradient(SG) algorithm for multivariable systems that can be parameterized into a class of multivariate linearregression models are studied, by using the stochastic process theory and the martingale theorem.The theoretical analysis indicates that the parameter estimation error given by the RLS algorithmapproaches to zero when the input signal is persistently exciting and the noise has zero mean vectorand fnite variance, and the parameter estimates given by the SG algorithm can converge to their truevalues even for non-stationary noises.2. For the multivariable linear systems disturbed by moving average noises, the recursive extended leastsquares algorithm and the extended stochastic gradient algorithm are presented. The performanceanalyses of the proposed algorithms under diferent conditions are studied by using the stochastic pro-cess theory and the martingale theorem. Simulation examples are given to illustrate the efectivenessof the algorithms.3. For the non-uniformly sampled multirate systems, the discrete-time input-output representations ofwhich are multivariable models, a coupled least squares (C-LS) algorithm and a partially coupledrecursive least squares (PC-RLS) algorithms are derived to estimate the model parameters with theadvantage of not involving the computation of a matrix inverse in each recursion step. The proposed(C-LS) algorithm is equivalent to the standard RLS algorithm and thus has the same convergenceproperties. Even the signals for the subsystems are not persistently exciting, the coupled identifcationalgorithms can still converge. Simulation examples verify the efectiveness of the algorithms.4. For multivariable linear regression models with autoregressive noises, a fltering-based recursive leastsquares (F-RLS) algorithm is presented. The idea is to transfer the system with a colored noise intoa system with a white noise by fltering the input-output data with a specifc flter, and then toidentify the fltered model and the noise model interactively. The flter is selected according to thenoise model structure. Since the algorithm transfers the identifcation model into two systems withmuch lower dimensions (one is the fltered system model and the other is the noise model), it hasless computational burden. The simulation results show that the F-RLS algorithm provides a higher accuracy of the parameter estimates under lower noise levels than the recursive generalized recursiveleast squares algorithm. When a batch of input-output data are obtained, a fltering based iterativeleast squares method is further derived.5. Based on the hierarchical identifcation principle, for a class of non-uniformly sampled systems and thegeneral dural-rate systems, whose discrete-time models are equivalent to multiple input single outputsystems and multi-input multi-output systems, respectively, the hierarchical least squares algorithmtogether with their convergence analyses are studied. The proposed algorithms can greatly save thecomputational cost. The performance analyses indicate that parameter estimates can converge totheir true values under certain conditions. The simulation tests confrm the convergence results. Thehierarchical identifcation principle is also employed to identify multivariable linear regression modelswith colored noises, compared with other methods, the hierarchical identifcation methods has theleast computational cost. A simulation confrms that the proposed algorithm is efective.