Abstract

Contrary to the average consensus, which means each state of multi-agent system converges to an average of individual initial conditions, we study a group behavior that obeys an "average of individual vector fields," which we call a blended dynamics. Under stability of the blended dynamics (not asking stability of individual agents), the behavior of heterogeneous multi-agent systems can be approximated by the solution to the blended dynamics. A following idea is to "design" the blended dynamics, from which individual heterogeneous multi-agents are assigned to different tasks. A few applications are discussed including distributed linear state estimation, estimation of the number of agents in a network, optimal power distribution of a smart-grid, robust synchronization of Van der Pol oscillators, and a distributed median solver. Since stability of the blended dynamics makes the initial conditions forgotten as time goes on, these algorithms are initialization-free and suitable for plug-and-play operation. At last, it is also emphasized that the obtained group behavior is robust to external disturbance and parametric variations in a certain sense.