Constrained optimal consensus in dynamical networks

Abstract

In this paper, an optimal consensus problem with local inequality constraints is studied for a network of single-integrator agents. The goal is that a group of single-integrator agents rendezvous at the optimal point of the sum of local convex objective functions. The local objective functions are only available to the associated agents that only need to know their own positions and of their neighbors. This point is supposed to be confined by some local inequality constraints. To tackle this problem, we integrate the primal-dual gradient-based optimization algorithm with a consensus protocol to drive the agents toward the agreed point that satisfies KKT conditions. The asymptotic convergence of the solution of the optimization problem is proven with the help of LaSalle's invariance principle for hybrid systems. A numerical example is presented to show the effectiveness of our protocol.