2 research outputs found
Cost-Optimal Switching Protection Strategy in Adaptive Networks
In this paper, we study a model of network adaptation mechanism to control
spreading processes over switching contact networks, called adaptive
susceptible-infected-susceptible model. The edges in the network model are
randomly removed or added depending on the risk of spread through them. By
analyzing the joint evolution of the spreading dynamics "in the network" and
the structural dynamics "of the network", we derive conditions on the
adaptation law to control the dynamics of the spread in the resulting switching
network. In contrast with the results in the literature, we allow the initial
topology of the network to be an arbitrary graph. Furthermore, assuming there
is a cost associated to switching edges in the network, we propose an
optimization framework to find the cost-optimal network adaptation law, i.e.,
the cost-optimal edge switching probabilities. Under certain conditions on the
switching costs, we show that the optimal adaptation law can be found using
convex optimization. We illustrate our results with numerical simulations
Optimal Design of Switched Networks of Positive Linear Systems via Geometric Programming
In this paper, we propose an optimization framework to design a network of
positive linear systems whose structure switches according to a Markov process.
The optimization framework herein proposed allows the network designer to
optimize the coupling elements of a directed network, as well as the dynamics
of the nodes in order to maximize the stabilization rate of the network and/or
the disturbance rejection against an exogenous input. The cost of implementing
a particular network is modeled using posynomial cost functions, which allow
for a wide variety of modeling options. In this context, we show that the
cost-optimal network design can be efficiently found using geometric
programming in polynomial time. We illustrate our results with a practical
problem in network epidemiology, namely, the cost-optimal stabilization of the
spread of a disease over a time-varying contact network.Comment: Accepted for publications in IEEE Transactions on Control of Network
System