Distributed constrained optimal consensus of multi-agent systems

We study a distributed optimal consensus problem of continuous-time multi-agent systems with a common state set constraint. Each agent is assigned with an individual cost function which is coercive and convex. A distributed control protocol is to be designed to guarantee a consensus, and in the meanwhile reach the minimizer of the aggregate cost functions within the constraint set. Three terms are included in the protocol: local averaging, local projection, and local subgradient with a diminishing but persistent gain. It is shown that the constrained optimal consensus can be achieved under a uniformly jointly connected communication network with bounded time-varying edge weights.