Realizing node-to-node connections is a basic functionality of communication networks. In some networks, like SDN, to perform this function nodes must have access to controllers – the devices (installed in selected node locations) necessary in the process of setting-up the connections. Hence, in case of an attack on a set of nodes, not only the directly attacked nodes are eliminated from service, but also the nodes that loose connection with the controllers located at the unaffected nodes). In order to increase network resilience against node-targeted attacks, a number of backup controllers (whose locations do not have to obey the stringent controller-controller and node controller delay constraints that have to be fulfilled by the primary controller locations) can be installed. In the paper we introduce a formulation of a general optimization problem addressing controllers placements that admit backup controllers in addition to primary controllers for increasing the resilience in question. A numerical study shows how the formulation can be used to investigate the benefits from the use of backup controllers.