Scalability and robustness in large scale networks and fundamental performance limits

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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.