  In this paper, we develop a compositional approach to abstraction and safety
synthesis for a general class of discrete time nonlinear systems. Our approach
makes it possible to define a symbolic abstraction by composing a set of
symbolic subsystems that are overlapping in the sense that they can share some
common state variables. We develop compositional safety synthesis techniques
using such overlapping symbolic subsystems. Comparisons, in terms of
conservativeness and of computational complexity, between abstractions and
controllers obtained from different system decompositions are provided.
Numerical experiments show that the proposed approach for symbolic control
synthesis enables a significant complexity reduction with respect to the
centralized approach, while reducing the conservatism with respect to
compositional approaches using non-overlapping subsystems.
