Distributed algorithm for a finite time horizon resource allocation over a directed network

Abstract

This work investigates a finite time horizon resource allocation problem under a strongly connected multi-agent network. In this network, each agent at each time is associated with a resource variable and a quadratic cost function. The objective is to minimise the total cost of all agents over the finite time horizon in a distributed manner, while enforcing a total amount of resources per time unit and per agent. The major challenge of this problem lies in the coupled equality constraints across the agents and time periods, which should be satisfied simultaneously in the end. In addition, the local information structure imposed by the digraph within the time horizon should be taken into account when solving the problem. This study develops a consensus-based multipliers decomposition method to solve the problem. The authors show that the convergence and optimality can be ensured provided that the digraph within the time horizon is strongly connected. Numerical simulations are presented to verify the effectiveness of the proposed algorithm.