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This thesis is concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. In this thesis, the author describes protocols to solve certain control and signal processing problems in this setting. It is demonstrated that a key challenge for such systems is the problem of computing averages in a decentralized way. Particularly, a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis is concerned with algorithms for the averaging problem and its generalizations. The author (i) derives the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) proves a lower bound identifying a fundamental barrier for averaging algorithms (iii) proposes a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model.
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