Simulating Robustness of Structural Controllability for Directed Networks under Multi-Round Edge Strategies

The study of structural controllability of control systems is a crucial property in the design and analysis of complex networks as well as networks which require a control relationship between nodes. The fundamental aim of attack vulnerability research is to safeguard electric power networks along-with their control systems as part of critical infrastructure systems. Such a system may have its structural control undermined or co-opted to hinder or hijack control if the entire network system is already known and understood by an attacker. A significant focus on the graph-theoretical interpretation of Kalman controllability has emerged as a concept linked to structural controllability that offers a powerful abstraction for understanding the structural properties of a control network and its critical elements. The determination of driver node sets that can monitor the whole network is therefore enabled, although it is a $W[{2}]$ -hard problem identifying these nodes. Indeed, problematic computational complexity is a feature of the various extant driver node identification techniques. Accordingly, this paper is highly motivated to adopt the power dominating set approach to explore how directed Erdős-Rényi networks are influenced by targeted iterative multiple-edge removal, in addition to the assessment of its effects on the robustness of network controllability from multiple structural vulnerabilities.