Abstract

The study of large scale and complex interconnected systems is of great importance in today’s networked world with applications ranging from distributed power generation to deep space exploration. A great challenge for these systems is to understand the interplay between the dynamic properties of the individual systems comprising the networks, the underlying information exchange network, and the interaction protocols governing the collective behavior. In this talk we will explore necessary and sufficient conditions for a network of passive dynamical systems to reach an output agreement, i.e., the trajectories of each system will synchronize. This leads to a refinement of classical passivity theory that we term maximal equilibrium passivity. We then show that the steady-state behavior of these systems are in fact solutions to a family of classic network optimization problems, and as a result we draw connections between notions of duality in static optimization to cooperative control. This network optimization perspective also leads to synthesis methods for controllers to guarantee the desired behavior of the network and provides new insights to classical problems such as feedback passivation.