Efficient space-time discretizations for tracking the boundaries of reachable sets

TL;DR

This paper introduces an efficient algorithm for approximating the boundaries of reachable sets in nonlinear control systems, reducing computational costs through adaptive discretization.

Contribution

It presents a novel boundary-tracking algorithm with non-uniform discretization for more efficient reachable set approximation.

Findings

Significantly reduces computational complexity.

Accurately tracks boundary of reachable sets.

Applicable to nonlinear control systems.

Abstract

The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and that chooses the temporal and spatial discretizations in a non-uniform way to reduce the computational complexity.