We present lazy abstraction-based controller synthesis (ABCS) for
continuous-time nonlinear dynamical systems against reach-avoid and safety
specifications. State-of-the-art multi-layered ABCS pre-computes multiple
finite-state abstractions of varying granularity and applies reactive synthesis
to the coarsest abstraction whenever feasible, but adaptively considers finer
abstractions when necessary. Lazy ABCS improves this technique by constructing
abstractions on demand. Our insight is that the abstract transition relation
only needs to be locally computed for a small set of frontier states at the
precision currently required by the synthesis algorithm. We show that lazy ABCS
can significantly outperform previous multi-layered ABCS algorithms: on
standard benchmarks, lazy ABCS is more than 4 times faster