Problems in Distributed Control And Sensing

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Intellectual Merit: Current interest in the control of distributed systems of all types has ledto a very rapid increase in the application of graph theoretic ideas to problems of analyzing and synthesizing a variety of desired behaviors such as swarming, rendezvousing, reaching a consensus, as well as well as a variety of sensing and communication tasks associated with search and rescue, environmental monitoring, security, etc. While this in-depth assault on these problems using a combination of graph theory and system theory is in its early stages, it is likely to significantly expand in the years to come. One line of research which illustrates the combined use of these concepts, is the recent theoretical work by a number of individuals which successfully explains the heading synchronization phenomenon observed in simulation by Vicsek, Reynolds and others more than a decade ago. Another is the recent surge of interest in the deployment and management of sensor networks of all types. In broad terms these are these are the areas within which we propose to work. In particular we propose to address distributed sensing and control on two fronts, both requiring the use both of traditional systems concepts and graph theory. First we propose to explore various versions of dynamic gossiping appropriate to a variety of applications in network management and cooperative, coordinated control. Second we propose to look in detail at a variety of issues concerned with the distanced-based localization of sensors in a large distributed network. In the area of gossiping, we will seek to construct a deterministic solution to the quantized gossiping problem. We will also attempt to develop a convergence theory for nonhomogeneous products of ?row sum 1? matrices with the aim of explaining {among other things} recent experimental results concerned with accelerated gossiping. In the area of sensor localization we will investigate the effects of measurement errors on the behavior of the recently developed ?sweeps? algorithm for sequential localization. By appealing to concepts developed in connection with the recently discovered {startling} characterization of global rigidity by Gortler et. al., we hope to significantly advance the newly devised divide and conquer approach to localizing a globally rigid network via decomposition and merging of local solutions. We will study the consequences of ?flip-ambiguities? in sensor localization and aim to derive necessary and sufficient for networks with such ambiguities to be localizable.Broader Impacts: This project will advance discovery and understanding while promoting teaching, training and learning in at least two different ways. First, graduate students involved in the project will be expected to attend and present there results at technical meetings. Second, project graduate students will contribute to and participate in a short course on the topic which we envision organizing and giving towards the end of the project. Two of the graduate students working on this project will be from under represented groups. This project will enhance infrastructure for research and education in at least two ways. First we expect to continue our cross-disciplinary collaboration with our environmental biologist colleagues with whom we?ve already been working for several years. Second, we expect to continue to collaborate with our experimentalist colleagues at Yale and UPENN who are building mobile sensor network test beds for trying out various control algorithms. Much of our research has been and will continue to be in close collaboration with B. D. O. Anderson and his group at Australian National University in Canberra. We hope to continue to contribute to broadening dissemination to enhance scientific and technological understanding by organizing and running boni fide interdisciplinary technical gatherings like the Block Island Workshop on Cooperative Control we co-organized and which took take place in June, 2003. Planning for such a meeting on Block Island in June, 2009 is already underway. We also expect to give overview talks on the subject such as the plenary presentation ?Multi-Agent Formationsand Sensor Networks? which we gave in December 2006 at the IEEE Conference on Decision and Control in San Diego.