Recovery of Structural Controllability into Critical Infrastructures under Malicious Attacks

The problem of controllability of networks can be seen in critical infrastructure systems which are increasingly susceptible to random failures and/or malicious attacks. The ability to recover controllability quickly following an attack can be considered a major problem in control systems. If this is not ensured, it can enable the attacker to create more disruptions as well as, like the electric power networks case, violate real-time restrictions and result in the control of the network degrading and its observability reducing significantly. Thus, the present paper examines structural controllability problem that has been in focus through the equivalent problem of the Power Dominating Set (PDS) introduced in the context of electrical power network control. However, the controllability optimisation problem can be seen as computationally infeasible regarding large complex networks because such problems are considered NP-hard and as having low approximability. Hence, the ability of structural controllability recoverability will be explored as per the PDS formulation, especially following perturbations in which an attacker with sufficient knowledge of the network topology is only able to completely violate the current driver control nodes of the original control network leading to a degradation of controllability of dependent nodes. The results highlight that the use of directed Laplacian matrix can be a useful approach for analysing structural controllability of a network. The simulation results show also that an increase of a connectivity probability of the distribution of links in Directed ER networks can minimise the number of driver control nodes which is highly desirable while monitoring the entire network.