A Network Optimization Approach to Cooperative Control Synthesis

The mathematical theory of nonlinear cooperative control relies heavily on notions from graph theory and passivity theory. A general analysis result is known about cooperative control of maximally equilibrium-independent systems, relating steady-states of the closed-loop system to network optimization theory. However, until now only analysis results have been proven, and there is no known synthesis result. This letter presents a controller synthesis procedure for a class of diffusively coupled dynamic networks. We use tools from network optimization and convex analysis to show that for a network composed of maximally equilibrium independent passive systems, it is possible to construct controllers on the edges that are maximally equilibrium independent output-strictly passive and achieve any desired formation. Furthermore, we show that this can be achieved with linear controllers. We also provide a simple controller augmentation procedure to allow for reconfiguration of the desired output formation without a redesign of the nominal control. We then apply the presented methods to reconstruct the well-known consensus algorithm, and to study formation control in networks of damped oscillators.