Utilizing Dependencies to Obtain Subsets of Reachable Sets

TL;DR

This paper introduces a method to efficiently extract subsets of reachable sets using state dependencies, significantly reducing computation time in applications like falsification, optimization, and safe maneuver synthesis.

Contribution

The paper presents a novel approach leveraging dependencies within previously computed reachable sets to quickly obtain over-approximative subsets without full re-computation.

Findings

Significant reduction in computation time for reachable set analysis.

Effective in falsification, optimization, and safe maneuver synthesis.

Demonstrated advantages over traditional re-computation methods.

Abstract

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few. In many of these applications, one requires to compute a reachable set starting within a previously computed reachable set. While it was previously required to re-compute the entire reachable set, we demonstrate that one can leverage the dependencies of states within the previously computed set. As a result, we almost instantly obtain an over-approximative subset of a previously computed reachable set by evaluating analytical maps. The advantages of our novel method are demonstrated for falsification of systems, optimization over reachable sets, and synthesizing safe maneuver automata. In all of these applications, the computation time is reduced significantly.