Controllability and Observability of Complex Systems
OVERVIEW: 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 studied be quantitatively, 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 of deducing 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.
READINGS:Liu, Y. Y., Slotine, J. J., & Barabasi, A. L. (2011). Controllability of complex networks. Nature, 473(7346), 167-173.
Zhao, C., Wang, W. X., Liu, Y. Y., & Slotine, J. J. (2014). Universal Symmetry in Complex Network Control. arXiv preprint arXiv:1403.0041.