Auxiliary Model Based Hierarchical Identification For Single-Input Multiple-Output Systems Using Output-Error Models

In industrial control, aerospace, astronomy, marine and many other areas, the object of study is generally more complex, such as single-input multiple-output system. The existing theories are often difficult to directly obtain the corresponding mathematical model by using observational data to determine the mathematical model of the object and its parameters. Based on the National Natural Science Foundation of China, this thesis studies the hierarchical identification for single-input multiple-output systems with output-error models. By using the hierarchical identification principle, the auxiliary model identification ideas, least square identification principle and the principle of stochastic gradient identification, the problem of a single-input multiple-output system identification is investigated. The main results are as follows:1. Firstly, the thesis describes the state space model of multiple-input multiple-output system leading to the single-input multiple-output state space model, and further describes the state space multiple-input multiple-output system which can be tranfromed into the transfer function of the standard output error model, which leads to the single-input multiple-output output error model with white noise. A theoretical basis is set up for the rest of this paper.2. For SIMO output error model with white noise, the hierarchical least squares algorithm and the hierarchical stochastic gradient algorithm with auxiliary model are developed. The basic idea is to decompose the SIMO system into two fictitious subsystems according to the hierarchical identification principle, with one containing a parameter vector and the other containing a parameter matrix. To solve the difficulty of the information matrix including immeasurable noise terms, the unknown noise terms are replaced by their residuals, which are computed through the preceding parameter estimates under the least squares princi-ple and the principle of stochastic gradient identification. Compared with recursive least squares algorithm, the computational burden of the presented algorithm is greatly reduced. The simulation results indicate that the proposed algorithm works quite well.3. For the parameter identification of the SIMO system with moving average noise, the hier-archical extended least squares algorithm and the hierarchical extended stochastic gradient algorithm are presented based on the hierarchical identification principle and the auxiliary model idea. The basic principle of the algorithm is similar to the single-input multiple-output model with white noise. The simulation results indicate that the proposed algorithm works quite well. 4. For the single-input multiple-output system with autoregressive moving average noise, the hierarchical generalized extended least squares identification algorithm and the hierarchi-cal generalized extended stochastic gradient identification algorithm are proposed based on the hierarchical identification principle and auxiliary model idea. The SIMO systems with moving average noise models can be regarded as special cases of the SIMO systems au-toregressive moving average noise models. Thus the SIMO systems autoregressive moving average noise models algorithm is more practical. The corresponding simulation examples are provided. Finally, the algorithms proposed can be extended to MIMO system.The thesis proposes several identification algorithms of the SIMO output error systems. The methods are verified by computer simulation examples. Some unsolving problems are briefly introduced in the final paper.