A Network Optimization Framework for Passive-Short Agents

We demonstrate that the presented network optimization framework cannot be used for passive-short agents, either because it is undefined, or because it predicts a wrong limit for the closed-loop system. The failure of the network optimization framework can be understood by the integral function for the agents being non-convex (when defined), or by the steady-state input-output relation for the agents being non-monotone. We will use this motivation to generalize the network optimization framework by augmenting the network optimization problems associated with the closed-loop system, and interpret the augmentation as a transformation of the agents.

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