Abstract
The controllability of networks is essential to maintain the components of the system at a desired state. Given inevitable failure or malicious attack, networks and their control structures must be designed optimally for performance in both healthy and damaged conditions. Significant research has been performed on the robustness of networks themselves, and the topological characteristics that heavily influence robustness. In this study, we critically analyse the robustness of the control cacti that govern the state of the constituents in four types of synthetic networks that have been developed to replicate the design advantages of particular natural networks. The average connectivity, and distribution of connections in the network proved highly influential on the physical attributes of control cacti built to regulate the network. Dependent on the type of attack or failure, the number of controls required, and structures of the cacti directly influence the controllability of a network. Therefore, the design of a network, the balance and availability of connections within a network structure, are highly critical attributes when designing a highly robust, controllable dynamical system.