Problems in Distributed Sensing and Control

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Intellectual Merit: Current interest in distributed control has led to 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 distributed averaging, search and rescue, environmental monitoring, security, etc. While this in-depth assault on these problems using a combination of graph theory and system theory has been underway for about a decade, it is likely to signicantly 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 focused on the coordination of networks of mobile robots and mobile sensors by means of rigidity-based formation control. Another is the recent surge of interest in the deployment and management of sensor networks of all types and in particular the development of distributed computational procedures for addressing basic numerical problems such as estimating parameters of a static linear system or solving a system of algebraic equations. In broad terms these are these are the problem 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 algorithms for controlling both directed and undirected rigid formations in a distributed manner. We will address the question of robustness to measurement errors and parameter discrepancies among agents and will attempt to find a way to avoid the recently discovered fundamental robustness issue with undirected formation control. In the area of distributed computation we will seek to develop distributed and asynchronous algorithms for solving unstructured systems of linear algebraic equations across a given network of autonomous agents assuming limited communication between agents and time-varying coefficent matrices. We will make use of recent advances in distributed optimization and also work by ourselves and others with dealing with special versions of this problem. 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 their 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 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 an group at Australian National University in Canberra. We will also continue our recent collaboration with the faculty at the University of Illinois. We hope to continue to contribute to broadening dissemination to enhance scientic and technological understanding by organizing and running boni-fide interdisciplinary technical gatherings like the Block Island Workshops on Cooperative Control we co-organized and which took take place in June, 2003 and again in June, 2009. We also expect to give overview talks on the subject such as the plenary presentation "Multi-Agent Formations and Sensor Networks" which we gave in December 2006 at the IEEE Conference on Decision and Control in San Diego and the keynote talk on "Deterministic Distributed Averaging" which we gave at the Chinese Control and Decision Conference in Mianyang, China in May 2011. Finally we are scheduled to give a 21 hour short course in May 2013 on Distributed Control at the EECI-HYCON2 Graduate School on Control in France. We gave a similar course at the same place last May.