Synchronisation of disturbed multi-agent systems

The paper investigates the synchronisation of disturbed multi-agent systems. The first result shows that dynamical local controllers have to be used to introduce the model of the disturbances into each of the extended agents. This result generalises the Internal-Model Principle from multivariable control to multi-agent systems with arbitrary communication structure. A test for the satisfaction of the Internal-Model Principle is provided. The second result is a necessary and sufficient condition for the asymptotic synchronisation of the disturbed agents. Third, the synchronisability of the agents is investigated and it is shown that additional dynamics in the local controllers may be necessary to make the extended agents synchronisable. Fourth, a design method is proposed to find a networked controller that synchronises the agent outputs and simultaneously attenuates the disturbances. Finally, the analysis of the resulting synchronous trajectory shows that the disturbance model included in the extended agents may dominate the overall system behaviour. The results are illustrated by numerical examples.