Sunday, February 17, 2013
Room 203 (Hynes Convention Center)
The ultimate proof of our understanding of biological or technological systems is reflected in our ability to observe and control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to observe the state and to control complex self-organized systems. Here I discuss the analytical tools to study the controllability of an arbitrary complex directed network, helping identify the set of driver nodes whose time-dependent control can guide the system's dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. I show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but dense and homogeneous networks can be controlled via a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the hubs. Finally, I show how these tools offer avenues to explore observability, helping identify the set of nodes whose monitoring allows us to reconstruct a system's full dynamics. Applications will be discussed from social to biological systems.
Work done in collaboration with Y. Liu, JJ Slotine, M. Posfai and T. Jia.