Scalability and robustness in large scale networks and fundamental performance limits

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.

Both industry and academia will benefit from this research. The novelty and significance lies in the fact that we address certain important features in network analysis and design, which, though essential from a practical perspective, introduce major complications in more conventional approaches. Data networks. From the early stages of the evolution of the Internet, it has been recognized that unrestricted access leads to low network utilization and high packet loss rates, a phenomenon known as congestion collapse. This has lead to the deployment of congestion control algorithms such as TCP and its different versions. These are variations of simple additive increase multiplicative decrease rules, usually tuned after analysis and extensive simulation on specific topologies, with no guarantees for their scalability. Nevertheless in the continuously evolving Internet, with large capacities and large, heterogeneous roundtrip times, current protocols have often turned out to be conservative; this is, for example, the case with long transatlantic links. A major challenge currently worldwide within the communications industry, is the development of improved algorithms which are scalable, with guarantees that they will be well behaved on an arbitrary interconnection. The proposed research will have a major impact in this direction: systematic methods for addressing this need for scalability will be developed. This will lead to improved versions of data network protocols where network resources will be better utilized. Flocking, vehicle platoons, sensor networks, power networks. These are all examples of networks where scalability is also important and therefore our analysis and design methodologies would be of value. The novelty in our setting is that the participating dynamics are heterogeneous, an important feature in such applications which renders the analysis much more demanding. Biological networks. Noise is ubiquitous in life processes within the cell; the importance of understanding the way this is suppressed within gene regulatory networks has been extensively reported by biologists in recent years, in corresponding leading international journals such as Nature, Science, PNAS. The fundamental limits we derive for noise suppression will be high impact contributions in this context bearing in mind the complexity of biological networks and the fact that these are often poorly characterized. More broadly, negative feedback is thought to be an integral part of many biological processes, and understanding the underlying principles is important. Academic beneficiaries. The notion of scalability in the domain control, the derivation of fundamental limitations for the suppression of intrinsic noise, as well as attempts to merge fundamental principles from control and information theory, provide elegant theoretical contributions within the context of control and information sciences. The way these results are applied is also of value to other academic communities such as computer scientists and biologists.