Mechanical and Civil Engineering Seminar

The question of how difficult or easy it is to control a certain network of interconnected dynamical agents is fundamental to understanding engineered or naturally occurring networks, such as vehicular formations or power grids amongst many others. I will argue that standard notions of stability and controllability as binary properties (e.g. a system is either stable or not), convergence rates, or even reachability analysis may fail to predict the behavior of large networks. These apparent difficulties motivate a notion of network controllability based on hard limits on performance in optimal control problems with structural constraints. While such problems are known to be generally intractable, I will show certain examples from vehicular platoons and power grids where informative and simple answers are possible in the asymptotic limit of large system size. This analysis gives asymptotic bounds on network performance and shows its dependence on both the complexity of individual node dynamics, as well as network connectivity. Some interesting connections between these results and the statistical mechanics of disordered media will be highlighted.