Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network

Distributed Channel Access for Control Over Unknown Memoryless Communication Channels

We consider the distributed channel access problem for a system consisting of multiple control subsystems that close their loop over a shared wireless network. We propose a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems. This is achieved by utilizing timers for prioritizing channel access with respect to a local cost which we derive by transforming the control objective cost to a form that allows its local computation. This property is then exploited for developing our distributed deterministic channel access scheme. A framework to verify the stability of the system under the resulting scheme is then proposed. Next, we consider a practical scenario in which the channel statistics are unknown. We propose learning algorithms for learning the parameters of imperfect communication links for estimating the channel quality and, hence, define the local cost as a function of this estimation and control performance. We establish that our learning approach results in collision-free channel access. The behavior of the overall system is exemplified via a proof-of-concept illustrative example, and the efficacy of this mechanism is evaluated for large-scale networks via simulations.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A Distributed Primal Decomposition Scheme for Nonconvex Optimization

In this paper, we deal with large-scale nonconvex optimization problems, typically arising in distributed nonlinear optimal control, that must be solved by agents in a network. Each agent is equipped with a local cost function, depending only on a local variable. The variables must satisfy private nonconvex constraints and global coupling constraints. We propose a distributed algorithm for the fast computation of a feasible solution of the nonconvex problem in finite time, through a distributed primal decomposition framework. The method exploits the solution of a convexified version of the problem, with restricted coupling constraints, to compute a feasible solution of the original problem. Numerical computations corroborate the results. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved