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、无处不在的通信系统是日常生活的重要组成部分，随着万物互联技术的出现，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全新的设计范式，因为它们是大规模的，并且涉及通信、“自然”（环境）网络以及控制的复杂交互作用。对如此复杂、互连和规模的系统进行无缝管理是令人生畏的。需要一种全新的方法来解决规模和复杂性问题。研究人员正在研究新的数学模型，用于比现有方法更大的系统的网络设计和优化。他们计划在认知无线电、无线身体区域传感网络和潜在的细菌种群模型等应用上展示他们的实用性。这些新方法有可能影响非常普遍的大规模网络的设计和控制，如生物网络、社会网络和智能电网。本研究开发了一个新的理论框架，通过分析、跟踪和控制与复杂系统相关的图上的马尔可夫过程来解决大规模系统设计的挑战。利用稀疏逼近理论，利用图小波表示这些大马尔可夫链中产生的相关性。典型的复杂系统会产生潜在的稀疏性，从而通过压缩的类感知方案实现降维。本研究通过为有向图设计新的图小波，结合新的稀疏逼近算法和为复杂系统量身定制的用于估计、通信和控制的控制方法，开发了新的稀疏技术，用于形式化建模、分析和优化时间演化的大规模系统。