Nonlinear protocols for distributed consensus in directed networks of dynamic agents

This paper deals with the distributed consensus problem of multi-agent systems. While existing work mainly considers the design of linear protocols, we derive nonlinear protocols for directed networks of dynamic agents with fixed and switched topologies, respectively. The obtained nonlinear protocols have the same effectiveness as the existing linear protocols, however they can satisfy the input constraints of real world physical systems, as well as the state value restrictions of agents, which ensure the smooth communication of the whole network and the correct data transmission among agents under the limited bandwidth. In contrast to most existing approaches that commonly use the Lyapunov function theory in order to prove the consensus problem, simple and effective mathematical methods are developed here for this purpose. Based on the equivalent infinitesimal functions and differentials as well as linear approximations as comparatively simple mathematical tools, we prove that the distributed consensus is asymptotically reachable and derive the group decision values. For balanced topology structures, these nonlinear protocols in particular guarantee that the agents asymptotically reach an average-consensus. Furthermore, the obtained protocols relax the constraints on the communication links among the agents. Finally, simulations comprising the vertical alignment maneuver of a team of unmanned aerial vehicles (UAVs) and the phase synchronization of three oscillators are studied, respectively. The simulation results underline that the developed nonlinear protocols are effective and feasible for distributed consensus in directed networks of dynamic multi-agent systems.