  This paper fully studies distributed optimal consensus problem in
non-directed dynamical networks. We consider a group of networked agents that
are supposed to rendezvous at the optimal point of a collective convex
objective function. Each agent has no knowledge about the global objective
function and only has access to its own local objective function, which is a
portion of the global one, and states information of agents within its
neighborhood set. In this setup, all agents coordinate with their neighbors to
seek the consensus point that minimizes the networks global objective function.
In the current paper, we consider agents with single-integrator and
double-integrator dynamics. We further suppose that agents movements are
limited by some convex inequality constraints. In order to find the optimal
consensus point under the described scenario, we combine the interior-point
optimization algorithm with a consensus protocol and propose a distributed
control law. The associated convergence analysis based on Lyapunov stability
analysis is provided.
