Alternating direction optimization algorithms for covariance completion problems
Alternating direction optimization algorithms for covariance completion problems
复制标题
协方差完成问题的交替方向优化算法
DOI：
10.1109/acc.2015.7170787
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
T. Georgiou
中科院分区：
文献类型：
--
作者：
A. Zare;M. Jovanović;T. Georgiou
非线性动力系统的二阶统计量可以通过实验或数值模拟得到。这些统计数据与理解基本物理有关，例如流体流动，并且对于开发低复杂性模型很有用。这些模型可用于控制设计和分析。在许多应用中，只有有限数量状态的某些二阶统计量可用。因此，以一种与线性化动力学一致的方式完成部分指定的协方差矩阵是有意义的。动力学对允许的强制相关性和状态统计施加结构约束。这类完井问题的解可以用来得到随机驱动的线性化模型。在这里，我们解决协方差补全问题。我们引入了一个将核范数与熵泛函相结合的优化准则。两者共同提供了一种数值稳定和可扩展的计算方法，该方法针对可以解释观察到的统计数据的随机强迫的低复杂性结构。我们开发了基于交替方向方法的定制算法，非常适合于大规模问题。
Second-order statistics of nonlinear dynamical systems can be obtained from experiments or numerical simulations. These statistics are relevant in understanding the fundamental physics, e.g., of fluid flows, and are useful for developing low-complexity models. Such models can be used for the purpose of control design and analysis. In many applications, only certain second-order statistics of a limited number of states are available. Thus, it is of interest to complete partially specified covariance matrices in a way that is consistent with the linearized dynamics. The dynamics impose structural constraints on admissible forcing correlations and state statistics. Solutions to such completion problems can be used to obtain stochastically driven linearized models. Herein, we address the covariance completion problem. We introduce an optimization criterion that combines the nuclear norm together with an entropy functional. The two, together, provide a numerically stable and scalable computational approach which is aimed at low complexity structures for stochastic forcing that can account for the observed statistics. We develop customized algorithms based on alternating direction methods that are well-suited for large scale problems.