Distributed resource coordination in networked systems described by digraphs

We consider a multicomponent system in which each component can receive/transmit information from/to components in its immediate neighborhood. Communication links between components are not required to be bidirectional, so that the information exchange between components in the system is in general described by a directed graph (digraph). Each component can contribute a certain amount of some resource (of the same type for each component), and the objective is for the components to distributively compute their individual resource contribution so as to collectively provide a requested amount of the resource. A further constraint is that each component's contribution is upper and lower bounded by locally known capacity constraints. In order to solve this resource coordination problem, we propose a distributed linear iterative algorithm in which each component maintains a set of values that are updated to be weighted linear combinations of its own previous value(s) and the values of the components it receives information from. Since the original choices of weights used by the components to perform the linear updates may not allow the components to solve the problem, the weights are allowed to adapt (also in a distributed fashion) as the algorithm progresses. Convergence of the proposed algorithm to a feasible solution is established analytically and demonstrated via examples.