Locally Interacting Hybrid Systems with Embedded Graph Grammars

In many cooperative control methods, the network topology influences the evolution of its continuous states. In turn, the continuous state may influence the network topology due to local restrictions on connectivity. In this paper we present a grammatical approach to modeling and controlling the switching of a system's network topology, continuous controllers, and discrete modes. The approach is based on embedded graph grammars, which restrict interactions to small subgraphs and include spatial restrictions on connectivity and progress. This allows us to direct the behavior of large decentralized systems of robots. The grammatical approach also allows us to compose multiple subsystems into a larger whole in a principled manner. In this paper, we illustrate the approach by proving the correctness of a cooperative control system called the load balanced multiple rendezvous problem