Consensus in Plug-and-Play Heterogeneous Dynamical Networks: A Passivity Compensation Approach

This paper investigates output consensus in heterogeneous dynamical networks within a plug-and-play framework. The networks are interconnected through nonlinear diffusive couplings and operate in the presence of measurement and communication noise. Focusing on systems that are input feedforward passive (IFP), we propose a passivity-compensation approach that exploits the surplus passivity of coupling links to locally offset shortages of passivity at the nodes. This mechanism enables subnetworks to be interconnected without requiring global reanalysis, thereby preserving modularity. Specifically, we derive locally verifiable interface conditions, expressed in terms of passivity indices and coupling gains, to guarantee that consensus properties of individual subnetworks are preserved when forming larger networks.

💡 Research Summary

The paper addresses the problem of achieving output consensus in large‑scale heterogeneous dynamical networks that must support plug‑and‑play (PnP) operations, i.e., the addition or removal of whole subnetworks without redesigning the entire system. The authors consider a set of agents whose dynamics are modeled as causal operators (H_i : L_2^e \rightarrow L_2^e). Each agent receives an input that is a nonlinear diffusive coupling of its own output, the outputs of its neighbors, and additive measurement/communication noises (w_i). The coupling functions (\phi_{ij}) are sector‑bounded, odd‑symmetric, and map zero to zero, which captures a wide class of nonlinear interconnections (including saturation, dead‑zone, etc.).

A central theoretical tool is Input‑Feedforward Passivity (IFP). An operator is IFP if there exist a scalar (\nu) (the passivity index) and a constant (\delta) such that (\langle u, H u\rangle \ge \nu |u|_2^2 + \delta) for all admissible inputs. Positive (\nu) indicates a surplus of passivity, while negative (\nu) denotes a shortage. Importantly, any asymptotically stable linear system can be represented with some IFP index, so the class is very broad.

The network is described by an undirected connected graph (G=(\mathcal N,\mathcal E)) with incidence matrix (D). By stacking the agents’ inputs, outputs and noises into vectors (U,Y,W) and defining (\Phi) as the block‑diagonal operator of the edge couplings, the overall interconnection can be compactly written as \