Lazy Abstraction-Based Control for Safety Specifications

TL;DR

This paper introduces a lazy, on-the-fly multi-layered abstraction approach for control synthesis in nonlinear systems, significantly reducing computation by selectively refining the state space during safety controller design.

Contribution

It proposes a novel lazy algorithm that computes state transitions dynamically, enabling more efficient safety controller synthesis for continuous nonlinear systems.

Findings

Reduces computational effort compared to traditional methods.

Enables larger state space exploration with coarser abstractions.

Demonstrates significant savings in controller synthesis time.

Abstract

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.