Distributed averaging with flow constraints

A network of storage elements is considered. Each storage element is an integrator which can exchange stored resource with neighboring elements. The flow between the elements as well as the amount of the resource that each element can store are subject to constraints. The problem of averaging the state of each element is addressed. The particularity of this problem compared to standard consensus-based averaging is that the elements exchange not only the information but also the stored resource. Thus the elements are controlled-coupled through the flow constraints. A distributed algorithm for flow control is proposed. The algorithm is non-iterative and does not require centralized design procedure. The proposed scheme guarantees asymptotic convergence of states of all nodes to the same value equal to the average of initial values.