Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper.Based on the centre manifold reduction technique,nonlinear consensus protocols are presented.We prove that a group of agents can reach a β-consensus,the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents.Moreover,we derive the conditions to guarantee that all the agents reach a β-consensus on a desired group decision value.Finally,a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed.Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.
