Proximal algorithms for large-scale statistical modeling and sensor/actuator selection
Proximal algorithms for large-scale statistical modeling and sensor/actuator selection
复制标题
用于大规模统计建模和传感器/执行器选择的近似算法
DOI：
10.1109/tac.2019.2948268
复制
发表时间：
2020
影响因子：
6.8
通讯作者：
Jovanovic, Mihailo R.
中科院分区：
文献类型：
--
作者：
Zare, Armin;Mohammadi, Hesameddin;Dhingra, Neil K.;Georgiou, Tryphon T.;Jovanovic, Mihailo R.
随机驱动动力系统的建模和控制中的几个问题可以归结为正则化的半定规划。我们研究了两个这样的代表性问题，并表明它们可以用类似的方式来表示。首先，在统计建模中，寻求通过适当和最小程度地扰动先前的动态来协调观察到的统计数据。第二种方法寻求最佳地选择可用传感器和执行器的子集以用于控制目的。为了解决大规模系统的建模和控制问题，我们使用近邻方法开发了一个统一的算法框架。我们的定制算法利用问题结构，并允许处理统计建模以及传感器和执行器选择，其规模远远大于当前通用解算器所能处理的范围。我们建立了近似梯度算法的线性收敛性，将所提出的近似算法与乘子交替方向法进行了对比，并给出了实例说明了该框架的优点和有效性。
Several problems in modeling and control of stochastically driven dynamical systems can be cast as regularized semidefinite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems, we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and the alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework.