Limits of Performance in Distributed Control

Perhaps one of the most important uses of optimal or robust control design is for characterizing plants rather than just designing optimal controllers. For example, it is well known that a plant’s right half plane poles and zeros impose fundamental performance limitations, and plant redesign can sometimes be informed by this characterization. Similar ideas have yet to be fully developed for distributed controllers and dynamical networks so as to characterize which networks are easy or difficult to control. I will present a collection of results motivated by those questions, particularly for large-scale systems and networks where certain systems exhibit scaling fragilities in the limit of large system sizes. These fragilities are exhibited as loss of robustness or increased sensitivities to disturbances. These fragilities can be fundamental to the structure of the control problem and are hard limits on performance once a control architecture is chosen. Some continuum models also exhibit similar fragilities in PDE systems, which serve as useful idealized models for finite, but large systems. I will discuss these interrelated issues and show examples from vehicular formations, power networks, as well as connections with condensed matter physics.  I will close by illustrating yet another fragility in a spatially distributed, active sensor network, namely the mammalian cochlea, where an instability mechanism appears to be related to certain clinical conditions.