Synchronization and control of complex networks via contraction, adaptation and evolution

Complex networked systems abound in Nature and Technology. They consist of a multitude of interacting agents communicating with each other over a web of complex interconnections. Flocks of birds, platoon of cooperating robots, swirling fishes in the Ocean are all examples whose intricate dynamics can be modeled in terms of three essential ingredients: (i) a mathematical description of the dynamical behavior of each of the agents in the network; (ii) an interaction (or coupling) protocol used by agents to communicate with each other and (iii) a graph describing the network of interconnections between neighboring agents. These three elements are actually mapped onto the mathematical model usually considered in the literature to describe a complex network which uses appropriate equations to describe the node dynamics, the coupling protocol and the network topology.