System theory over random consensus networks: Controllability and optimality properties

In this paper we present a framework for designing feedback controllers for directing a group of agents adopting consensus-type algorithms over random networks. In this direction, we first examine the pertinent necessary and sufficient conditions for controllability and observability of protocols over random networks. We then proceed to explore conditions on the underlying distribution for guaranteeing optimal infinite horizon linear quadratic regulators. The implementation of the proposed methodology is then discussed via an illustrative example.