Non-deterministic reconfiguration of tree formations

We consider a network of mobile agents in an initially unknown acyclic network configuration and the problem of reconfiguring them into a desired network topology and formation geometry while maintaining connectivity in an asynchronous network. We model the system and solution as an embedded graph grammar and use a method of lexicographically ordered Lyapunov functions to show the system converges non-deterministically regardless of the initial network structure and the order of the communication events.