Duality and Network Theory in Passivity-based Cooperative Control
For control theorists and network engineers, this work provides a unifying framework linking cooperative control and network optimization, but the results are theoretical and not yet demonstrated on practical benchmarks.
This paper establishes a formal connection between passivity-based cooperative control and convex network optimization, showing that networks with maximal equilibrium independent passivity asymptotically solve dual optimization problems, and illustrates the theory on a nonlinear traffic model that exhibits asymptotic clustering.
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.