This article addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.

中文翻译：

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使用神经网络控制器验证自治系统的安全性

本文解决了使用神经网络 (NN) 控制器验证自治系统安全性的问题。我们专注于具有 sigmoid/tanh 激活的 NN，并利用 sigmoid/tanh 是二次微分方程的解这一事实。这允许我们将 NN 转换为等效的混合系统，并将问题转换为混合系统验证问题，可以通过现有工具解决。此外，我们通过使用具有最坏情况误差界限的泰勒级数来逼近 sigmoid，从而提高了所提出方法的可扩展性。最后，我们提供了对四个基准的评估，包括与基于混合整数线性规划以及星集的替代方法的比较。