统计学习理论是研究训练样本有限情况下机器学习规律的理论，系统辨识是现代控制理论的一个重要分支。最新研究结果表明，统计学习理论和系统辨识相结合可以使二者在理论、方法等方面互相丰富。在线性系统的辨识研究中，系统极点的确定是科学与工程研究的热点，其又与复变函数的有理逼近问题紧密联系，有理正交基Takenaka-Malmquist在其中扮演着十分重要的角色。本项目将首先利用统计学习理论和复分析相关知识，研究有理函数极点的刻画和确定问题，估计线性系统的极点。然后构造基于Takenaka-Malmquist基的机器学习算法，得到解析函数用Taknenaka-Malmquist基的线性组合来逼近的有效方法，最终实现线性时不变系统的系统辨识和应用。本质上，该算法可以看作是自适应傅里叶分解（AFD）算法的一个扩充。我们期望本项目的研究能够推动逼近论的发展，推广学习理论的应用领域，为系统辨识提供新的解决思路。

The statistical learning is the theory of machine learning law in the limited case of training samples, system identification is an important branch of modern control theory. The new research results show that the combination of statistical learning theory and system identification can make them rich in theory and method. In the identification of linear systems, the determination of the poles is a hot topic in science and engineering, which is closely related to the rational approximation of complex functions, and the rational orthogonal base Takenaka-Malmquist plays a very important role. This project will first use the related knowledge of statistical learning theory and the complex analysis to study the description and determination problem of rational function poles and estimate the poles of linear system. Then, a machine learning algorithm based on Takenaka-Malmquist is constructed, and an effective method is obtained to approximate the analytic function with the linear combination of Taknenaka-Malmquist base. Finally the system identification and application of the linear time invariant system are realized. In essence, the algorithm can be regarded as an extension of Adaptive Fourier Decomposition (AFD) algorithm. We hope that the research of this project can promote the development of the approximation theory, popularize the application field of learning theory, and provide a new way to solve the system identification.