  This paper presents a class of passivity-based cooperative control problems
that have an explicit connection to convex network optimization problems. The
new notion of maximal equilibrium independent passivity is introduced and it is
shown that networks of systems possessing this property asymptotically approach
the solutions of a dual pair of network optimization problems, namely an
optimal potential and an optimal flow problem. This connection leads to an
interpretation of the dynamic variables, such as system inputs and outputs, to
variables in a network optimization framework, such as divergences and
potentials, and reveals that several duality relations known in convex network
optimization theory translate directly to passivity-based cooperative control
problems. The presented results establish a strong and explicit connection
between passivity-based cooperative control theory on the one side and network
optimization theory on the other, and they provide a unifying framework for
network analysis and optimal design. The results are illustrated on a nonlinear
traffic dynamics model that is shown to be asymptotically clustering.
