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.
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