Estimation Methods For Nonlinear Systems With Multirate Sampling

System identifcation and model parameter estimation are the basis of control prob-lems. At present, nonlinear system identifcation has become a hot research feld. Themultirate sampling are caused by data loss in the transmission of information, hard-ware damage in storing data, sampling frequency limitations of sampling devices and soon. Therefore, the study of identifcation methods for nonlinear systems with multiratesampling is of universal signifcance and has wide application prospects. By using theauxiliary model, the key term separation principle and the coupled identifcation con-cept, this dissertation aims to develop identifcation methods for nonlinear systems withmultirate sampling. The main contributions are summarized as follows.1. Based on the auxiliary model method, the least square recursive algorithm isderived for the dual-rate Hammerstein nonlinear output error model. The convergenceof algorithm is analyzed by using the martingale convergence theorem. In order to im-prove the accuracy and the convergence rate of stochastic gradient parameter estimationalgorithm, multi-innovation stochastic gradient algorithm are developed for the dual-rateHammerstein nonlinear output error model.2. To solve the identifcation problem of Hammerstein output error systems with theunmeasurable variables in the information vector, the least-squares and gradient based it-erative algorithms are presented by replacing the unmeasurable variables with their corre-sponding iterative estimates. To estimate parameters of the presented model, an auxiliarymodel-based recursive least-squares algorithm is derived by replacing the unmeasurablevariables in the information vector with their corresponding recursive estimates.3. Based on the auxiliary model method, the least square recursive algorithmis derived for the Hammerstein nonlinear output error auto regressive moving average(HOEARMA) system. The multiple stage recursive least squares identifcation methodis developed for the HOEARMA system. The basic idea is to decompose a HOEARMAmodel into multiple submodels and then to identify the parameters of each submodel, re-spectively. The dimensions of the involved covariance matrices in each submodel becomesmall and thus the proposed algorithm has a high computational efciency.4. The signal identifcation model is studied according the data sampled by non-uniform updating rates. The iterative gradient algorithms are derived for the two casesof known and unknown signal fundamental frequency. From the point of view of reducingthe dimension of the covariance matrix, the two stage recursive least squares algorithm isdeveloped for the signal model with non-uniform sampling by using decomposition tech-nique. According to the multi-innovation theory, the multi-innovation stochastic gradient algorithm is derived for for the signal model with non-uniform sampling.In summary, this thesis studies and derives the identifcation algorithms for nonlinearsystems and the signal model with multirate sampling, the efectiveness of the algorithmsis illustrated by Matlab simulations.