This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a target distribution accounting for the network topology. We exploit the specific structure of the problem, characterized by the computation of implicit gradient steps, and formulate an approach based on discretized flows. As a result, our proposed algorithm relies on the iterative computation of constrained Wasserstein barycenters. We show how the proposed method finds approximate solutions to the network transport problem, taking into account the topology of the network, the capacity of the communication channels, and the capacity of the individual nodes.

Este artículo se centra en resaltar la vasta utilidad de la teoría de juegos, en particular aquella basada en la vertiente dinámica evolutiva, dentro del modelado y control de sistemas dinámicos complejos y de gran escala. Concretamente, y a través de ejemplos claros y de aplicación real, se motiva el uso de las dinámicas poblacionales para el modelado de sistemas ciberfísicos, así como los modelos dinámicos de pago para complementar un sistema de control en lazo cerrado con restricciones (físicas y operacionales), cuyos objetivos se alinean con la distribución dinámica de recursos y el alcance de equilibrios generalizados de Nash.

We study a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be “transported” to a target distribution accounting for the network topology. We exploit the specific structure of the problem, characterized by the computation of implicit gradient steps, and formulate an approach based on discretized flows. As a result, our proposed algorithm relies on the iterative computation of constrained Wasserstein barycenters. We show how the proposed method finds approximate solutions to the network transport problem, taking into account the topology of the network, the capacity of the communication channels, and the capacity of the individual nodes.

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of O(1/k 2 ). Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.