  We present a lazy version of multi-layered abstraction-based controller
synthesis (ABCS) for continuous-time nonlinear dynamical systems against safety
specifications. State-of-the-art multi-layered ABCS uses pre-computed
finite-state abstractions of different coarseness. Our new algorithm improves
this technique by computing transitions on-the-fly, and only when a particular
region of the state space needs to be explored by the controller synthesis
algorithm for a specific coarseness. Additionally, our algorithm improves upon
existing techniques by using coarser cells on a larger subset of the state
space, which leads to significant computational savings.
