Teams and games for distributed consensus

The problem of synthesizing linear dynamic feedback controllers which achieve distributed finite-time consensus for networks of multiple agents described by fixed connectivity graphs is considered. The techniques of teams and games are employed in synthesizing these controllers. Under the situations where the connectivity graph is known to every agent or to a central authority a priori, the network behaves as a team and the solution procedure involves posing a finite-horizon decentralized control problem and converting it to a static convex optimization problem via linear quadratic team-theoretic notions. The dynamic feedback controller thus synthesized optimizes a transient performance measure and guarantees consensus within a minimal number of steps.;Extending these results to situations where the networks are described by connectivity graphs which are not known at the outset to any of the agents or to a central authority, the problem of optimal distributed consensus is formulated as a decentralized linear quadratic game where the agents minimize their own local costs by sequentially learning the network connectivity and generating local decisions. A distributed protocol based on online optimization and linear dynamic feedback is shown to achieve an equilibrium with respect to these local costs. For the cases of unknown undirected (bidirectional) graphs the protocol produces an optimal performance with time-optimal finite-time consensus. The control protocol is formed by coupling and jointly optimizing the tasks of network learning and network control so that the states can be steered to the desired consensus value.;Under unknown general directed graphs a similar distributed control protocol exhibits a near-optimal finite-time consensus. Several classes of directed graphs for which the controller performs optimally in space and/or in time have been identified. On the other hand, counterexamples show that due to the difficulties inherent to dealing with general directed graphs, no control policy is uniformly optimal over all directed graphs.