  We consider the problem of a dynamical network whose dynamics is subject to
external perturbations (`attacks') locally applied at a subset of the network
nodes. We assume that the network has an ability to defend itself against
attacks with appropriate countermeasures, which we model as actuators located
at (another) subset of the network nodes. We derive the optimal defense
strategy as an optimal control problem. We see that the network topology, as
well as the distribution of attackers and defenders over the network affect the
optimal control solution and the minimum control energy. We study the optimal
control defense strategy for several network topologies, including chain
networks, star networks, ring networks, and scale free networks.
