Abstract:

A large body of literature has investigated the structure and functions of complex dynamical networks.

Typical examples of dynamics that have been considered include epidemics, traffic and congestion, synchronization, evolutionary games, cascading failures, et cetera. Applications of these studies are relevant to biological networks, such as food webs, neuronal circuits, and gene-regulatory networks, as it appears Nature has often exploited network structures to organize itself at many different levels and scales.

More recently, increasing attention has been devoted to strategies to control the dynamics of these networks, i.e., how control inputs can be injected in some of the network nodes to achieve a desired dynamical performance. These studies have leveraged the vast body of literature on the characterization of network dynamics, but also the concepts and techniques developed under the broad umbrella of control theory. While much of the research in control theory focuses on controlling individual systems, the same techniques can be applied to complex dynamical networks. With the emergence of this new area of study, it becomes possible to advance research in a new direction, from describing complex systems to controlling them.

I will review some recent results on control of networks that have leveraged the algebraic theory of controllability due to Kalman and the theory of structural controllability due to Lin. For controllable networks, I will discuss possible control techniques, including the design of optimal control strategies aimed at minimizing the control energy. Finally, I will present preliminary results from my group.