Index-Free Multi-agent Systems: An Eulerian Approach

Since the properties of systems comprising many homogeneous agents may be expected to be independent of how the agents happen to be indexed, it should be possible to formulate and solve multi-agent control problems in an index-free way. In this paper we provide such an approach, based on an indicator distribution representation, which results in integro-differential dynamics that parallel and extend those obtained within the traditional indexed formulations. Conservation and stability properties are proven; a compatible geometric structure is constructed for the indexed representation; and a discrete analogue is presented which illustrates that for certain problems the Eulerian viewpoint results in very simple controllers.