Lazy Abstraction-Based Controller Synthesis

TL;DR

Lazy abstraction-based controller synthesis (ABCS) for nonlinear systems improves efficiency by constructing abstractions on demand, significantly outperforming previous methods in standard benchmarks.

Contribution

Introduces lazy ABCS that constructs abstractions on demand, reducing computational effort compared to multi-layered ABCS.

Findings

Lazy ABCS is over 4 times faster on benchmarks.

Constructs abstractions locally for relevant states.

Outperforms previous multi-layered ABCS methods.

Abstract

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.