Growing controllable networks via whiskering and submodular optimization

The topology of a network directly influences the behaviour and controllability of dynamical processes on that network. Therefore, the design of network topologies is an important area of research when examining the control of distributed systems. We discuss a method for growing networks known as whiskering, as well as generalizations of this process, and prove that they preserve controllability. We then use techniques from submodular optimization to analyze optimization algorithms for adding new nodes to a network to optimize certain objectives, such as graph connectivity.