Decentralized Abstractions For Multi-Agent Systems Under Coupled Constraints

The goal of this report is to define abstractions for multi-agent systems with feedback interconnection in their dynamics. 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 coupled constraints, and additional free inputs which we exploit in order to accomplish high level tasks. In the first part of 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. Finally, we extend the framework by appropriately modifying the latter conditions in order to ensure multiple discrete transitions which provide the possibility for motion planning, given higher level specifications.