A fully distributed approach to resource allocation problem under directed and switching topologies

This paper addresses the distributed resource allocation problem for a network of multiple agents with directed and time-varying communication topologies. Suppose that the total amount of resources is a constant, represented by an equality constraint, and that the amount of resources allocated to each agent is subject to an inequality constraint, called the state constraint. We then aim to solve it in a fully distributed manner. By introducing a surplus variable to store the residue at each step due to the state constraint on each agent, a distributed iteration algorithm is proposed to solve the distributed resource allocation problem subject to the state constraints. It is shown that the algorithm converges globally provided that the communication graph is jointly strongly connected. The most promising characteristic of the algorithm is that the parameters used in the iteration by each agent depend only on local knowledge of the in-degree and out-degree of itself, yet the algorithm converges globally for a time-varying communication network.