On the Steady-State Inverse-Optimality of Passivity-based Cooperative Control

We consider a passivity based cooperative control problem, and show that the steady-state behavior of the networked system is intimately related to a family convex network optimization problems. This result provides a duality interpretation between the different signals in the cooperative control system. In particular, we show that the input and output signals as well as the dynamic controller state and controller output are pairs of dual variables. The presented results facilitate an optimal controller design in networked systems. We show how this novel interpretation leads the way to an optimal routing design in distribution networks.