Herding Positive, Complex Networks
For researchers studying control of complex networks (e.g., biological, robotic), this work provides a new framework and practical tools for network control when strict controllability is not required.
This paper introduces herdability as a more flexible alternative to controllability for complex networks, focusing on positive systems. It develops methods for adding inputs to ensure herdability and proposes a centrality measure to select the best single node for herding.
The problem of controlling complex networks is of interest to disciplines ranging from biology to swarm robotics. However, controllability can be too strict a condition, failing to capture a range of desirable behaviors. Herdability, which describes the ability to drive a system to a specific set in the state space, was recently introduced as an alternative network control notion. This paper considers the application of herdability to the study of complex networks under the assumption that a positive system evolves on the network. The herdability of a class of networked systems is investigated and two problems related to ensuring system herdability are explored. The first is the input addition problem, which investigates which nodes in a network should receive inputs to ensure that the system is herdable. The second is a related problem of selecting the best single node from which to herd the network, in the case that a single node is guaranteed to make the system is herdable. In order to select the best herding node, a novel control energy based herdability centrality measure is introduced.