Regularization and Feedback Passivation in Cooperative Control of Passivity-Short Systems: A Network Optimization Perspective

In this letter, we establish a connection between cooperative control of passivity-short systems, and the regularization of a pair of dual network optimization problems. We build upon existing works that established, under a passivity requirement, an equivalence between the steady-state behavior of diffusively coupled network system and the solutions to a pair of convex-dual optimization problems. We show that when the agents are passivity-short, the resulting optimization problems are no-longer convex. By introducing a regularization term to the problem, we then establish that this corresponds to a feedback passivation of each system via an appropriately chosen linear output-feedback gain. We also obtain conditions on the regularization term such that the resultant closed system possess the so-called maximally equilibrium-independent passivity property and exhibits a solution to their network-level interactions. Finally, we illustrate theoretical results with two case studies.