Synchronization of multi-agent systems with heterogeneous controllers

This paper studies synchronization in a multi-agent system, which is defined as a situation where all the agents in a group are required to achieve a common velocity direction. The agents are assumed to be coupled through controller gains that are not necessarily identical or homogeneous, which addresses a practical scenario where the gains may vary nominally due to minor implementation errors or drastically due to major faults or errors. The paper analyzes the effect of heterogeneous gains on the common velocity direction at which the system of agents synchronizes. Conditions under which heterogeneous controller gains result in a synchronized formation are derived and it is shown that the resulting common velocity direction lies in the conic hull of the initial velocity vectors of agents. A detailed analysis of the two agents system shows that there exists a less restrictive condition on heterogeneous gains that results in synchronization. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Both all-to-all and limited communication topologies are considered. Simulations are given to support the theoretical findings.