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 passive systems, relating steady-states of the closed-loop system to optimal solutions of certain static convex network optimization problems. This relation has many applications in various areas of multi-agent systems, e.g. model-free control, network identification, and fault detection and isolation.
However, when trying to apply the framework to passive-short systems directly, it fails, as the cost function in the optimization problem becomes non-convex, or even undefined. We show the network optimization framework can be extended to output-passive short systems by regularizing the said optimization problems, inducing a passivizing feedback term on the agents. We explore two methods of doing so. We then study systems with general shortage of passivity, showing that a passivizing transformation can always be found by an analogous regularization process. We exemplify our results by case studies.
