A Randomized Algorithm for Parsimonious Model Identification
A Randomized Algorithm for Parsimonious Model Identification
复制标题
DOI：
10.1109/tac.2017.2723959
复制
发表时间：
2018-02
影响因子：
6.8
通讯作者：
Burak Yılmaz;K. Bekiroglu;C. Lagoa;M. Sznaier
中科院分区：
文献类型：
--
作者：
Burak Yılmaz;K. Bekiroglu;C. Lagoa;M. Sznaier
识别简约模型通常是一个“难”的非凸问题。可用的方法通常依赖于松弛，如群套索或核规范最小化。此外，将稳定性和模型顺序约束纳入此类方法的形式化中会导致计算复杂性的大幅增加。在这些挑战的激励下，在本文中，我们提出了简化线性时不变系统识别算法，旨在识别低复杂性模型，这些模型i)包含系统的先验知识（例如，稳定性），ii)允许具有缺失/非均匀测量的数据，以及iii)能够使用从具有不同未知初始条件的系统的多次运行中获得的数据。所提出的随机化算法基于原子范数的概念，为从大量噪声数据中识别稀疏模型提供了一种数值上有效的方法。
Identifying parsimonious models is generically a “hard” nonconvex problem. Available approaches typically rely on relaxations such as Group Lasso or nuclear norm minimization. Moreover, incorporating stability and model order constraints into the formalism in such methods entails a substantial increase in computational complexity. Motivated by these challenges, in this paper we present algorithms for parsimonious linear time invariant system identification aimed at identifying low-complexity models which i) incorporate a priori knowledge on the system (e.g., stability), ii) allow for data with missing/nonuniform measurements, and iii) are able to use data obtained from several runs of the system with different unknown initial conditions. The randomized algorithms proposed are based on the concept of atomic norm and provide a numerically efficient way to identify sparse models from large amounts of noisy data.