TIRA: Toolbox for Interval Reachability Analysis

TL;DR

TIRA is a Matlab toolbox that provides scalable interval over-approximation methods for reachable sets of nonlinear systems, emphasizing simplicity and extensibility over precision.

Contribution

It introduces a modular Matlab library with multiple reachability methods for nonlinear systems, enabling easy addition of new techniques.

Findings

Contains four reachability methods for nonlinear systems.

Designed for scalability and ease of extension.

Focuses on simplicity over accuracy.

Abstract

This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main strength of interval-based reachability analysis is its simplicity and scalability, rather than the accuracy of the over-approximations. The current implementation of TIRA contains four reachability methods covering wide classes of nonlinear systems, handled with recent results relying on contraction/growth bounds and monotonicity concepts. TIRA's architecture features a central function working as a hub between the user-defined reachability problem and the library of available reachability methods. This design choice offers increased extensibility of the library, where users can define their own method in a separate function and add the function call in the hub function.