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系统辨识(7)：递阶辨识原理与方法
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基金项目:

国家自然科学基金(60973043)


System identification.Part G：Hierarchical identification principle and methods
Author:
  • DING Feng

    DING Feng

    School of Internet of Things Engineering, Jiangnan University, Wuxi 214122;Control Science and Engineering Research Center, Jiangnan University, Wuxi 214122;Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education), Jiangnan University, Wuxi 214122
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    摘要:

    递阶辨识是系统辨识的一个重要分支.递阶辨识原理是在大系统递阶控制的"分解-协调原理"基础上发展起来的,它不仅能够解决参数数目多、维数高、大规模系统辨识算法计算量大的问题,而且能够解决结构复杂的双线性参数系统、多线性参数系统以及非线性系统的辨识问题.首先介绍递阶辨识原理和线性方程组Ax=b的著名雅可比迭代和高斯-赛德尔迭代,给出了线性方程组的迭代方法族;其次将雅可比迭代思想和递阶辨识原理用于研究一般矩阵方程和耦合矩阵方程的递阶梯度迭代求解方法和递阶最小二乘迭代求解方法;再次介绍了方程误差模型的两阶段最小二乘辨识方法(一个简单的递阶辨识方法)和线性回归模型的递阶最小二乘辨识方法;最后研究了类多变量CARMA系统的递阶辨识方法.

    Abstract:

    Hierarchical identification is an important branch of system identification.The hierarchical identification principle is developed on the bisis of the "decomposition-coordination principle" in the hierarchical control for a large-scale system.It is able to not only solve problems that the identification algorithms require heavy computational burden for a lareg-scale systems with many parameters and high dimensions problem,but also solve identification problems for bilinear-parameter systems,multi-linear-parameter systems and nonlinear systems with complex structures.In this paper,firstly we describe the hierarchical identification principle,the Jacobi iteration and Gauss-Seidel iteration for linear systems with a set of equations Ax=b,and give the family of iterative methods for linear equations;secondly,we study hierarchical least squares based and hierarchical gradient based iterative algorithms for general matrix equations and coupled matrix equations in the light of the Jacobi iteration and the hierarchical identification principle;thirdly,we present a two-stage recursive least squares algorithm(i.e.,a simple hierarchical least squares algorithm) for equation error models and a hierarchical least squares identification algorithm for linear regression models.Finally,the hierarchical identification methods are introdiced for multivariable CARMA-like systems using the hierarchical identification principle.

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丁锋.系统辨识(7)：递阶辨识原理与方法[J].南京信息工程大学学报(自然科学版),2012,4(2):97-124
DING Feng. System identification. Part G：Hierarchical identification principle and methods[J]. Journal of Nanjing University of Information Science & Technology, 2012,4(2):97-124

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