  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. We will describe
protocols to solve certain control and signal processing problems in this
setting. We will demonstrate that a key challenge for such systems is the
problem of computing averages in a decentralized way. Namely, we will show that
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 will be concerned with algorithms for the averaging problem and
its generalizations. We will (i) derive the fastest known averaging algorithms
in a variety of settings and subject to a variety of communication and storage
constraints (ii) prove a lower bound identifying a fundamental barrier for
averaging algorithms (iii) propose 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.
