Decentralized abstractions for feedback interconnected multi-agent systems

The purpose of this paper is to define abstractions for multi-agent systems under coupled constraints. In the proposed decentralized framework, we specify a finite or countable transition system for each agent which only takes into account the discrete positions of its neighbors. The dynamics of the considered systems consist of two components. An appropriate feedback law which guarantees that certain performance requirements (e.g., connectivity) are preserved and induces the coupled constraints, and additional free inputs which are exploited for the accomplishment of high level tasks. In this work we provide sufficient conditions on the space and time discretization for the abstraction of the system's behaviour which ensure that we can extract a well posed and hence meaningful transition system.