NeTS: Medium: A Sparse Decomposition Framework for Complex System Design and Analysis

NeTS：Medium：复杂系统设计和分析的稀疏分解框架

• 批准号: 1410009
• 负责人: Urbashi Mitra
• 金额: $ 82.57万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1410009&HistoricalAwards=false
• 关键词: NeTS; Medium; Sparse; Decomposition; Framework

Large scale, pervasive communication systems are an important part of everyday life and, with the emergence of the Internet of Everything technology, are becoming an essential part of our infrastructure. Future communication systems necessitate significantly new design paradigms because they are large scale and involve a complex interaction of communications, "natural" (environmental) networks as well as control. The seamless management of a system of this complexity, interconnection, and scale is daunting. A fundamentally new approach is needed to tackle the issues of scale and complexity. The investigators are studying novel mathematical models for network design and optimization for systems of much larger size than those that are tractable with current methods. They are planning to demonstrate their utility on applications such as cognitive radio, wireless body area sensing networks and potentially models for bacterial populations. The new methods have the potential to impact the design and control of very general, large-scale networks such as biological, social networks and the SmartGrid.This research develops a novel theoretical framework to address the challenges of large scale system design by analyzing, tracking, and controlling Markov processes over graphs associated with complex systems. The correlation induced in these large Markov chains is exploited via sparse approximation theory employing graph wavelets for representation. Typical complex systems induce an underlying sparsity that enables dimensionality reduction via compressed sensing-like schemes. This research develops new sparse techniques for formal modeling, analysis and optimization of large-scale systems that evolve temporally, by designing novel graph wavelets for directed graphs, in combination with new sparse approximation algorithms and control methods tailored to the complex systems for estimation, communication and control.

大规模，普遍的通信系统是日常生活的重要组成部分，随着一切技术的互联网的出现，它正在成为我们基础设施的重要组成部分。未来的通信系统需要大量新的设计范例，因为它们是大规模的，并且涉及通信的复杂相互作用，“自然”（环境）网络和控制。对这种复杂性，互连和规模的系统的无缝管理令人生畏。需要一种新的方法来解决规模和复杂性问题。研究人员正在研究用于网络设计的新型数学模型，并针对尺寸大得多的系统进行优化。他们计划在认知无线电，无线身体区域传感网络以及潜在的细菌种群模型上展示其实用性。这些新方法有可能影响非常通用的大规模网络的设计和控制，例如生物学，社交网络和SmartGrid。这项研究开发了一个新颖的理论框架，通过分析，跟踪和控制与复杂系统相关的图表来应对大规模系统设计的挑战。这些大马尔可夫链中引起的相关性通过稀疏近似理论利用，采用图形小波进行表示。典型的复杂系统诱导了一种潜在的稀疏性，该稀疏度可以通过压缩感测定方案降低维度。这项研究开发了新的稀疏技术，用于对大型系统的形式建模，分析和优化，这些系统通过设计用于定向图的新型图形小波，结合新的稀疏近似算法和针对复杂系统量身定制的用于估算，通信和控制的复杂系统的控制方法。