Recovery of Structural Controllability for Control Systems

Two of the fundamental problems of control systems theory are controllability and observability, and designing control systems so that these properties can be satisfied or approximated sufficiently. However, it is prudent to assume that attackers will not only be able to subvert measurements but also control. Moreover, advanced adversaries with an understanding of the control system may seek to take over control of the entire system or parts thereof, or deny the legitimate operator this capability; the effectiveness of such attacks has been demonstrated in previous work. Therefore, we argue that such attacks cannot be ruled out entirely given the likely existence of unknown vulnerabilities, increasing connectivity of nominally air-gapped systems, and even supply chain issues. The ability to rapidly recover control after an attack has been initiated or the detection of an adversary’s presence is therefore critical. In this paper we study the problem of structural controllability that has recently re-gained substantial attention through the equivalent problem of the Power Dominating Set introduced by Haynes in the context of electrical power network control. However, these problems are known to be NP-hard with poor approximability. Given their relevance to many networks, especially for power networks, we study strategies for the efficient restoration of