TERA: A Unified Taylor Model Enabled Reachability Analysis Framework

Abstract

Reachability analysis of safety-critical systems requires computing rigorous enclosures of all possible state trajectories. Taylor Model (TM)-based methods have proved effective at mitigating the so-called wrapping effect which leads to overly conservative enclosures of reachable sets. However, existing tools are often hard to extend or focused on narrow system classes (e.g. deterministic systems modelled by ODEs, or hybrid systems). We develop TERA: a Python-native framework for TM-based reachability analysis of continuous, hybrid and stochastic systems within a single symbolic-numeric workflow. TERA is free and open-source, enabling rapid prototyping of reachability analysis techniques with rigorous enclosures. At present, our implementation is able to compute tight reachable set over-approximations for non-linear ODEs and hybrid systems on difficult benchmark problems, and already supports analysis of continuous-time stochastic systems. Our goal is to develop a robust open-source Python infrastructure for rigorous reachability analysis supporting a broad class of systems, including stochastic hybrid systems.