Convergent Under-Approximations of Reachable Sets and Tubes for Linear Uncertain Systems

TL;DR

This paper introduces a convergent iterative method to under-approximate finite-time reachable sets and tubes for linear time-varying uncertain systems, improving safety analysis in control systems.

Contribution

It presents a novel iterative approach for under-approximating reachable sets of LTV systems with uncertain initial conditions and inputs, ensuring convergence in Hausdorff distance.

Findings

Method converges in Hausdorff distance

Applicable to linear time-varying systems with uncertainties

Validated through numerical examples

Abstract

In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable time-varying system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets which results in convergent under-approximations in the sense of Hausdorff distance. We illustrate our approach through two numerical examples.