  This paper proposes networked dynamics to solve resource allocation problems
over time-varying multi-agent networks. The state of each agent represents the
amount of used resources (or produced utilities) while the total amount of
resources is fixed. The idea is to optimally allocate the resources among the
group of agents by minimizing the overall cost function subject to fixed sum of
resources. Each agents' information is restricted to its own state and cost
function and those of its immediate in-neighbors. This is motivated by
distributed applications such as mobile edge-computing, economic dispatch over
smart grids, and multi-agent coverage control. This work provides a fast
convergent solution (in comparison with linear dynamics) while considering
relaxed network connectivity with quantized communication links. The proposed
dynamics reaches optimal solution over switching (possibly disconnected)
undirected networks as far as their union over some bounded non-overlapping
time-intervals has a spanning-tree. We prove feasibility of the solution,
uniqueness of the optimal state, and convergence to the optimal value under the
proposed dynamics, where the analysis is applicable to similar 1st-order
allocation dynamics with strongly sign-preserving nonlinearities, such as
actuator saturation.
