Analyzing the Robustness of Network Controllability against Malicious Attacks

Description

Network controllability is a fundamental issue that must be determined and guaranteed before one can consider how to control a complex dynamical network in engineering applications. When the network is subject to random or intentional attacks, its controllability needs resilience by means of supplying backup control inputs, which presents the robustness to the network: the less new control inputs are needed, the more robust the network controllability is. The present proposal aims to address this theoretically fundamental and technically challenging question for some specific complex networks, for which controllability and its robustness can be precisely defined and characterized, paving the way to studying more general and advanced configurations of complex networks. Specifically, a measure of robustness is defined for the network controllability as the effort to withstand failures due to malicious attacks, so as to recover the network controllability from the destruction, by the percentage of new control inputs versus the size of the network. Both node-removal and edge-removal attacks in random and intentional fashions will be investigated. Some optimal network building blocks, namely basic motif structures, for best controllability robustness will be identified and characterized. Typical directed networks, such as directed Henneberg networks, Random Triangular Networks (RTN), and Random Rectangular Networks (RRN), will be simulated and analyzed using machine learning-based optimization techniques for their best robustness of controllability. To that end, a general directed complex network with many loops will be studied to confirm the essential role of loops in the network controllability robustness. Then, for theoretical analysis and robust network design, controllability robustness bounds will be estimated. Both lower bound and upper bound for the network robustness of directed Henneberg networks, as well as directed 3-motif RTN and directed 4-motif RRN, will be established.  In many engineering applications, it is key to determine, before a design, whether or not a network is controllable and how robust it would be against malicious and destructive attacks. This project will address this important issue, hence will have significant impact in the interdisciplinary scientific fields of complex networks and control theory, as well as network design optimization, which has rapidly evolved in the past decade towards real applications in industrial assembly automation and biological systems such as brain science and biological neuronal systems.