Abstract: The emergence of synchronization in complex networks of coupled oscillators is a pervasive topic in numerous scientific disciplines including biology, physics, chemistry, and engineering. A coupled-oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among the oscillators. These two ingredients give rise to rich dynamic behaviors that have fascinated the scientific community for decades. In this talk I will present joint work with Florian Dorfler and John Simpson on novel algebraic conditions for synchronization. The results exploit elegant connections among the theory of coupled oscillators, the graph-theoretical properties of electric circuits, and multiagent dynamical systems. Our results are relevant in the context of future smart grids subject to renewable stochastic power sources: assessing the existence, stability, optimality, and robustness of synchronous states is a pervasive topic in the study and operation of power networks.
Biosketch: Francesco Bullo received the Laurea degree in Electrical Engineering from the University of Padova in 1994, and the Ph.D. degree in Control and Dynamical Systems from the California Institute of Technology in 1999. From 1998 to 2004, he was affiliated with the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign. He is currently a Professor with the Mechanical Engineering Department at the University of California, Santa Barbara. His students' papers were finalists for the Best Student Paper Award at the IEEE Conference on Decision and Control (2002, 2005, 2007), and the American Control Conference (2005, 2006, 2010). He is the coauthor of the book "Geometric Control of Mechanical Systems" (Springer, 2004) and of the book "Distributed Control of Robotic Networks" (Princeton, 2009). His main research interest is multi-agent networks with application to robotic coordination, distributed computing and power networks. For more information on Prof. Bullo's research please see his website at http://motion.me.ucsb.edu