Wavelet 模型在系统辨识中的应用

Application of Wavelet Model in System Identification

小波分析理论是近年发展起来的一个新的数学分支．为了研究Ｗａｖｅｌｅｔ分析理论在控制问题中系统辨识领域的应用，提出了Ｗａｖｅｌｅｔ模型并分析了其结构和特征．同时，引入Ｌａｇｕｅｒｒｅ模型作为与Ｗａｖｅｌｅｔ模型进行对比研究的对象，剖析了两者的相同之处及差异．通过将Ｌａｇｕｅｒｒｅ模型与Ｗａｖｅｌｅｔ模型同时应用于构造具有延时因子的线性系统的模型中，经分析比较，发现Ｗａｖｅｌｅｔ模型优越于Ｌａｇｕｅｒｅ模型．

In order to study the application of wavelet in system identification of control field, a Wavelet model is presented and its structure and feature are studied. At the same time, Laguerre model which is widely used in system identification and function approximation is introduced as a comparison object, and both similarities and differences between Wavelet model and Laguerre model are analyzed. The Wavelet model and Laguerre model representations for identification of linear system with timedelay are discussed respectively. Through the comparison analysis, it is found that the performance of Wavelet model is superior to Laguerre model, which can offer some theoretical basis for further research work in the future.