  In this paper, distributed convex optimization problem over non-directed
dynamical networks is studied. Here, networked agents with single-integrator
dynamics are supposed to rendezvous at a point that is the solution of a global
convex optimization problem with some local inequality constraints. To this
end, all agents shall cooperate with their neighbors to seek the optimum point
of the networks global objective function. A distributed optimization algorithm
based on the interior-point method is proposed, which combines an optimization
algorithm with a nonlinear consensus protocol to find the optimum value of the
global objective function. We tackle this problem by addressing its
sub-problems, namely a consensus problem and a convex optimization problem.
Firstly, we propose a saturation protocol for the consensus sub-problem. Then
to solve the distributed optimization part, we implement a centralized control
law, which yields the optimum value of the global objective function, in a
distributed fashion with the help of a distributed estimator. Convergence
analysis for the proposed protocol based on the stability theory for
time-varying nonlinear systems is included. A simulation example is given at
the end to illustrate the effectiveness of the proposed algorithm.
