Multi-group consensus via pinning control with non-linear heterogeneous agents

The agents connected by networks are capable to reach a prescribed state if only a small fraction of them are controlled with feedback information. The present work tries to stabilize groups of non-linear agents in a directed network onto a stable state with several equilibriums. The agent dynamics can be identical or heterogeneous. But the agents in the same group share a same non-linear model. The conditions to reach multiple consensus states are provided under both non-switching and switching topologies. The maximum number of heterogeneous equilibriums is discussed. It is proved theoretically and by simulations that under certain conditions, pinning control can lead a multi-group network to reach a multi-valued consensus state.