Simultaneous Identification of Fractional-order System Structure and Order and Parameters Based on Alternately Transforming Condensed Information Matrix
基于信息压缩矩阵交替变换的分数阶系统结构、阶次与参数的同时辨识方法

The identification theory and method of fractional system is an important research direction in the field of fractional-order control which has drawn much research attention recently. However, the relevant study rarely involved the structure and order of fractional-order systems. Firstly, the colored noise model of linear fractional-order system is discussed. Then, the condensed information matrix whose information vectors have shift structure character is constructed, and the theoretical analysis and its proof about the condensed information matrix factorization and transform are also given. On this basis, an identification algorithm by transforming the condensed information matrix alternately and extracting relevant information from this matrix is proposed, and the decision criteria for the optimal estimation model structure and order are discussed, so the structure and order and parameters of the fractional-order system time domain model can be identificated simultaneously. The simulation study indicates that this method can obtain satisfactory identification results, and also has better ability of noise suppression. Not only the structure and order of the system model but also those of the noise model can be identified accurately.