Heterogeneous Multi-Agent Systems: Reduced-Order Synchronization and Geometry

This technical note studies the geometry of multiple interacting heterogeneous multi-agent systems (MAS), where the agent dynamics may not be the same. A detailed geometric theory is given here based on the Kalman observable form decomposition and a further characterization of that portion of the leader's dynamics that is hidden within the dynamics of each agent. The output regulator equations are expressed in the new coordinates and are seen to be composed of an observable part and an unobservable part. These new geometric ideas are used to design efficient reduced-order synchronizers that guarantee synchronization of the outputs of all agents to a leader. It is shown that synchronization of heterogeneous MAS can be achieved if each agent has a mix of a dynamic synchronizer for the part of the leader's dynamics that is not contained in the agent's dynamics, and a static feedback synchronizer for the part that is.