Scalability and robustness in large scale networks and fundamental performance limits

所提出的研究将对大规模复杂网络的分析和综合做出贡献：通过扩展控制理论的工具，将发展基本理论并解决重要应用。网络存在于整个物理和生物世界，但如今它们也弥漫在我们的社会和日常生活中。这些著名的例子包括互联网、电力网络、金融市场；许多其他新兴应用，如成排的车辆、卫星编队、传感器网络；以及自然界中发现的例子，从蜂群现象到基因调控网络。将解决的主要挑战是：1.保证健壮和可扩展的大规模异质网络的工程设计。生物网络的逆向工程。我们想要工程的网络的一个显著特征是可伸缩性，它属于系统和控制方面更传统的领域。可伸缩性在这里指的是，随着网络随着异类代理的添加或移除而发展，必须保持网络的稳定性和健壮性。例如，想象一下，每次有新的计算机/路由器进入互联网时，都必须重新设计拥塞控制算法。拟议研究的一个主要目标是开发满足这种可伸缩性需求的方法，即能够通过仅基于局部交互的条件来保证整个任意网络的稳健稳定性。在此上下文中的先前结果表明，通过利用互连结构，这确实是可能的。然而，许多问题仍然没有得到回答。其目的是在一个共同的坚实的理论框架上，将不那么保守的线性结果与相应的更保守的非线性方法合并。这将导致非保守的设计，因此具有实际意义。这些方法将对Internet拥塞控制协议的设计产生重大影响；改进的、不那么保守的算法将导致更好地利用网络资源。同样的抽象理论也可以保证其他网络的稳健稳定性，在这些网络中，可扩展性是一个问题，其新颖性在于参与动态的异构性。这些领域包括蜂群现象、无人驾驶车辆编队的协调、传感器网络中的分布式计算以及其他相关应用，如车辆排和电力网络中的同步运行。该项目还将通过对细胞内内在随机性的分析，在分子水平上为生物网络的逆向工程做出贡献。细胞中的生命是由偶然决定的；噪声无处不在，其来源从波动的环境到由于单个分子的随机出生和死亡而引起的内在波动。噪声的很大一部分是内在的(而不是相加的)，这一事实给控制理论方法论带来了重大挑战。如何使用反馈来抑制这些波动，相关的权衡和限制是什么，以及自然如何在特定的机制中如此有效地处理这些问题？我们的研究将通过开发分析已知配置的工具来解决这些问题，但更重要的是，通过推导适用于任意反馈策略的基本限制来解决这些问题。这些硬的性能界限是这些过程的简单特征的结果，例如存在延迟和噪声反馈通道。利用这一理论将研究特定的反馈机制，如细菌中的质粒复制控制，从而更好地理解潜在的功能。更广泛地说，反馈存在于许多生物过程中，理解潜在的原理是重要的。

The proposed research will make a contribution towards the analysis and synthesis of large scale complex networks: fundamental theory will be developed and important applications will be addressed, by extending tools from control theory. Networks are present throughout the physical and biological world, but nowadays they also pervade our societies and everyday lives. Such celebrated examples include the Internet, power networks, financial markets; many other emerging applications such as platoons of vehicles, satellite formations, sensor networks; and also examples found in nature, ranging from flocking phenomena to gene regulatory networks. Major challenges that will be addressed are:1. The engineering of large scale heterogeneous networks that are guaranteed to be robust and scalable.2. The reverse engineering of biological networks.A distinctive feature of the networks we would like to engineer, which falls outside more traditional domains in systems and control, is that of scalability. Scalability here refers to the fact that network stability and robustness must be preserved as the network evolves with the addition or removal of heterogeneous agents. Imagine, for example, having to redesign congestion control algorithms each time a new computer/router enters the Internet. A main objective of the proposed research is to develop methodologies for addressing this need for scalability, i.e. be able to guarantee robust stability of the entire arbitrary network by conditions on only local interactions. Previous results in this context show that this is indeed possible by exploiting interconnection structure. Nevertheless many questions still remain unanswered. The aim is to merge less conservative linear results, with corresponding more conservative nonlinear approaches on a common solid theoretical framework. This will lead to non-conservative designs, which are thus of practical interest. These methodologies will have a significant impact on the design of Internet congestion control protocols; improved, less conservative algorithms will lead to a better utilization of the network resources. The same abstract theory can also guarantee robust stability of other networks where scalability is an issue, with the novelty lying in the heterogeneity of the participating dynamics. These include flocking phenomena, coordination of unmanned vehicle formations, distributed computations in sensor networks and other related applications such as vehicle platoons and synchronous operation in power networks.The proposed project will also make a contribution towards the reverse engineering of biological networks at the molecular level, by focusing on the analysis of intrinsic stochasticity within the cell. Life in the cell is dictated by chance; noise is ubiquitous with its sources ranging from fluctuating environments to intrinsic fluctuations due to the random births and deaths of individual molecules. The fact that a substantial part of the noise is intrinsic (and not additive) provides a major challenge in control theoretic methodologies. How can feedback be used to suppress these fluctuations, what are the associated tradeoffs and limitations, and how does nature manage to handle these so efficiently in specific mechanisms? These are questions that will be addressed with our research by developing tools for analyzing known configurations, but more importantly, by deriving fundamental limitations that hold for an arbitrary feedback policy. These hard performance bounds are a result of simple features of these processes such as the presence of delays and noisy feedback channels. Specific feedback mechanisms, such as plasmid replication control in bacteria, will be studied using this theory, thus leading to a better understanding of the underlying functionality. More broadly, feedback is present in many biological processes and understanding the underlying principles is important.