Network Feedback Passivation of Passivity-Short Multi-Agent Systems

In this paper, we propose a network-optimization framework for the analysis of multi-agent systems with passive-short agents. We consider the known connection between diffusively-coupled maximally equilibrium-independent passive systems, and network optimization, culminating in a pair of dual convex network optimization problems, whose minimizers are exactly the steady-states of the closed-loop system. We propose a network-based regularization term to the network optimization problem and show that it results in a network-based feedback using only relative outputs. We prove that if the average of the passivity indices is positive, then we convexify the problem, passivize the agents, and that steady-states of the augmented system correspond to the minimizers of the regularized network optimization problem. We also suggest a hybrid approach, in which only a subset of agents sense their own output, and show that if the set is nonempty, then we can always achieve the same correspondence as above, regardless of the passivity indices. We demonstrate our results on a traffic model with non-passive agents and limited GNSS reception.