动力系统可辨识性研究综述

A survey of identifiability problems in dynamical systems

中文关键词  可辨识性  动力系统  模型结构  动力学网络  系统辨识  网络重构

英文关键词  identifiability  dynamical systems  model structures  dynamical network  system identification  network reconstruction

中文摘要

      “可辨识性”是模型能否由观测数据唯一确定的性质, 在经济学、生物学、化学、控制科学等多学科中被系统性地研究. 近二十年来, 随着动力系统复杂性急剧增加, 将系统建模为动力学网络的研究愈加普遍, 网络可辨识性也越来越受到学界关注. “可辨识性”不仅是系统辨识的理论保证, 而且可以作为建模中实验设计、数据采集等的理论指导. 本文综述动力系统的可辨识性问题, 首先, 给出了可辨识性问题的描述及相关定义. 根据模型不同类别, 本文对线性时不变系统与系统矩阵相关的可辨识性经典结论进行了阐述, 并对非线性时不变系统的输入输出方法、输出相等方法等可辨识性主要研究方法进行阐述. 针对激励矩阵和观测矩阵的4种不同情况, 本文对动力学网络模型的可辨识性问题和代表性成果进行综述. 最后, 本文讨论了其仍需解决的问题和未来的研究方向.

英文摘要

      Identifiability is the property that whether a model can be uniquely determined by observational data, which is systematic studied in economics, biology, chemistry and control. In the past two decades, with the complexity of dynamical systems increasing dramatically, it is becoming more popular to model a system as a dynamical network, and identifiability of dynamical networks is attracting much attention from the academic community. Identifiability is not only a theoretical guarantee for system identification, but also a theoretical guide for experimental design and data collection in modeling. This work reviews identifiability problems of dynamical systems. Firstly, the problems of identifiability and some related definitions are given. Then classical conclusions on the identifiability of linear time-invariant systems. General approaches, such as input-output method and output-equality method, to study the identifiability for nonlinear systems are presented. The problem of identifiability and representative research of dynamical network are introduced for four different cases of excitation and observation matrices. The survey ends with discussions on related problems to be solved in future.