Simple synchronization protocols for heterogeneous networks: beyond passivity

Synchronization among autonomous agents via local interactions is one of the benchmark problems in multi-agent control. Whereas synchronization algorithms for identical agents have been thoroughly studied, synchronization of heterogeneous networks still remains a challenging problem. The existing algorithms primarily use the internal model principle, assigning to each agent a local copy of some dynamical system (internal model). Synchronization of heterogeneous agents thus reduces to global synchronization of identical generators and local synchronization between the agents and their internal models. The internal model approach imposes a number of restrictions and leads to sophisticated dynamical (and, in general, nonlinear) controllers. At the same time, passive heterogeneous agents can be synchronized by a very simple linear protocol, which is used for consensus of first-order integrators. A natural question arises whether analogous algorithms are applicable to synchronization of agents that do not satisfy the passivity condition. In this paper, we study the synchronization problem for heterogeneous agents that are not passive but satisfy a weaker input feedforward passivity (IFP) condition. We show that such agents can also be synchronized by a simple linear protocol, provided that the interaction graph is strongly connected and the couplings are sufficiently weak. We demonstrate how stability of cooperative adaptive cruise control algorithms and some microscopic traffic flow models reduce to synchronization of heterogeneous IFP agents.