Consensus of Multi-Agents with Event-Based Nonlinear Coupling over Time-Varying Digraphs

This work addresses the consensus problem of a group of agents coupled via nonlinear locally passive functions over a time-varying network. A consensus protocol is designed which is solely dependent on an agent’s own instantaneous state and the states broadcasted from its neighbors. A time-dependent triggering condition is defined to govern the broadcasting of one’s state to all its neighbors. Information exchange only occurs when the triggering condition is met, as a result, communication overhead can be greatly reduced. It is mathematically proved that consensus is reachable and Zeno behavior is excluded if the union of the underlying graphs over any time interval of certain length admits a directed spanning tree. The proposal is applicable for various kinds of networks, such as continuously time-varying network, switching network, blinking network, and its effectiveness is confirmed with numerical examples.