  In this paper, we focus on mitigating the computational complexity in
abstraction-based controller synthesis for interconnected control systems. To
do so, we provide a compositional framework for the construction of
abstractions for interconnected systems and a bottom-up controller synthesis
scheme. In particular, we propose a notion of approximate composition which
makes it possible to compute an abstraction of the global interconnected system
from the abstractions (possibly of different types) of its components. Finally,
by leveraging our notion of approximate composition, we propose a bottom-up
approach for the synthesis of controllers enforcing decomposable safety
specifications. The effectiveness of the proposed results is demonstrated using
two case studies (viz., DC microgrid and traffic network) by comparing them
with different abstraction and controller synthesis schemes.
