A distributed methodology for approximate uniform global minimum sharing

Abstract

The paper deals with the distributed minimum sharing problem, in which a network of decision-makers - exchanging information through a communication network - computes the minimum of some local quantities of interest in a distributed and decentralized way. The problem is equivalently cast into a cost-coupled distributed optimization problem, and an adjustable approximate (or sub-optimal) solution is presented which enjoys several properties of crucial importance in applications. In particular, the proposed solution is scalable in that the dimension of the state space does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial condition) asymptotic stability result is provided, as well as an attractiveness property towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence is also recovered at the price, however, of loosing uniformity of the convergence with respect to the initial time.