Scalability and robustness in large scale networks and fundamental performance limits

拟议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，将开发基本理论并解决重要应用问题。网络存在于整个物理和生物世界，但如今它们也渗透到我们的社会和日常生活中。这些著名的例子包括互联网、电网、金融市场；许多其他新兴应用，如车辆排，卫星编队，传感器网络；也有自然界的例子，从群体现象到基因调控网络。将解决的主要挑战是：1。保证鲁棒性和可扩展性的大规模异构网络工程。生物网络的逆向工程。我们想要设计的网络的一个显著特征是可扩展性，它不属于更传统的系统和控制领域。这里的可伸缩性指的是，随着网络随着添加或删除异构代理而发展，必须保持网络的稳定性和健壮性。想象一下，例如，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。所提出的研究的一个主要目标是开发解决这种可扩展性需求的方法，即能够通过仅在局部交互的条件下保证整个任意网络的鲁棒稳定性。先前在这方面的结果表明，通过利用互连结构，这确实是可能的。然而，许多问题仍未得到解答。目的是在一个共同的坚实的理论框架上合并不太保守的线性结果和相应的更保守的非线性方法。这将导致非保守设计，因此具有实际意义。这些方法将对互联网拥塞控制协议的设计产生重大影响；改进的、不那么保守的算法可以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鲁棒稳定性，其中可扩展性是一个问题，其新颖性在于参与动态的异质性。其中包括群集现象、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，如车辆排和电网中的同步运行。提议的项目还将对分子水平上的生物网络逆向工程做出贡献，重点是分析细胞内的内在随机性。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产生的内在波动。事实上，很大一部分噪声是固有的（而不是附加的），这对控制理论方法提出了重大挑战。如何使用反馈来抑制这些波动，相关的权衡和限制是什么，以及大自然如何在特定机制中如此有效地处理这些波动？这些问题将在我们的研究中得到解决，通过开发分析已知配置的工具，但更重要的是，通过推导出任意反馈策略的基本限制。这些硬性能边界是这些过程的简单特征（如延迟和噪声反馈通道的存在）的结果。具体的反馈机制，如细菌中的质粒复制控制，将使用这一理论进行研究，从而更好地理解其潜在的功能。更广泛地说，反馈存在于许多生物过程中，理解其基本原理很重要。

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.