  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.
