One often wishes for the ability to formally analyze large-scale systems-typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This paper tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this paper to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs.

中文翻译：

---

Krylov 子空间中输入不确定的大型线性系统的可达性分析


人们常常希望能够正式分析大型系统——然而，通常，人们既可以正式分析一个相当小的系统，也可以非正式地分析一个大型系统。本文试图进一步缩小线性系统可达性分析的性能差距。可达性分析可以捕获动态系统的整套可能的解决方案，从而用于证明永远不会达到不安全状态；这需要充分考虑任意变化的不确定输入，因为传感器噪声或干扰通常不遵循任何模式。我们在本文中使用 Krylov 方法来计算大规模线性系统的可达集。虽然 Krylov 方法之前已用于可达性分析，但我们克服了之前输入必须（分段）恒定的限制。因此，我们可以针对有界但任意变化的输入计算具有数千个状态变量的可达系统集。