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arXiv 1807.01739math.OCcs.AIcs.LGcs.SYeess.SY
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大规模统计建模和传感器/执行器选择的近端算法

Proximal algorithms for large-scale statistical modeling and sensor/actuator selection

Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California(南加州大学明希赫电子与计算机工程系);Numerica Corporation(Numerica公司)

Armin Zare, Hesameddin Mohammadi, Neil K. Dhingra, Tryphon T. Georgiou, Mihailo R. Jovanović

AI总结:

本文提出了一种统一的近端算法框架,用于解决大规模系统建模与控制中的正则化半定规划问题,通过近端方法实现了对统计建模和传感器/执行器选择的高效处理,展示了算法的线性收敛性和有效性。

摘要:

若干在随机驱动动态系统建模与控制中的问题可以被表述为正则化半定规划。我们考察了两个具有代表性的此类问题,并展示了它们可以以类似的方式进行表述。第一个问题在统计建模中寻求通过适当且最小的扰动来协调观测统计数据。第二个问题则旨在为控制目的最优选择可用的传感器和执行器子集。为了应对大规模系统的建模与控制,我们开发了一种统一的算法框架,利用近端方法。我们的定制算法利用问题结构,使得能够处理统计建模以及传感器和执行器选择,比当前通用求解器可以处理的规模大得多。我们建立了近端梯度算法的线性收敛性,对比了所提出的近端算法与交替方向乘子法,并提供了示例以说明我们框架的优势和有效性。

英文摘要:

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite 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 alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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