The ultimate proof of our understanding of complex systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered systems towards a desired state, a framework to control complex systems is lacking. In this talk I will show that many dynamic properties of complex systems can be quantitatively studied, via a combination of tools from control theory, network science and statistical physics. In particular, I will focus on two dual concepts, i.e. controllability and observability, of general complex systems. Controllability concerns our ability to drive the system from any initial state to any final state within finite time, while observability concerns the possibility to deduce the system’s internal state from observing its input-output behavior. I will show that by exploring the underlying network structure of complex systems one can determine the driver (or sensor) nodes that with time-dependent inputs (or measurements) will enable us to fully control (or observe) the whole system.
Dr. Yang-Yu Liu is presently an Assistant Professor of Medicine at Harvard Medical School, and an Associate Scientist at Brigham and Women’s Hospital. Dr. Liu received his Ph.D in Physics from the University of Illinois at Urbana-Champaign in 2009. His current research interests focus on complex networks, control theory and systems biology. His work “Controllability of Complex Networks” has been featured as a cover story in Nature (May 12, 2011) and received broad media coverage including Nature News&Views, Science News&Analysis, ScienceNews, ScienceDaily, Wired, PHYSORG, and Faculty of 1000. His recent work “Observability of complex systems” has been featured as a cover story in the Proceedings of the National Academy of Sciences of the U.S.A (Feb. 12, 2013).