Complex dynamical systems rely on the correct deployment and operation of numerous components, with state-of-the-art methods relying on learning-enabled components in various stages of modeling, sensing, and control at both offline and online levels. This article addresses the runtime safety monitoring problem of dynamical systems embedded with neural-network components. A runtime safety state estimator in the form of an interval observer is developed to construct the lower bound and upper bound of system state trajectories in runtime. The developed runtime safety state estimator consists of two auxiliary neural networks derived from the neural network embedded in dynamical systems, and observer gains to ensure the positivity, namely, the ability of the estimator to bound the system state in runtime, and the convergence of the corresponding error dynamics. The design procedure is formulated in terms of a family of linear programming feasibility problems. The developed method is illustrated by a numerical example and is validated with evaluations on an adaptive cruise control system.

中文翻译：

---

启用神经网络的动态系统的运行时安全监视。

复杂的动态系统依赖于众多组件的正确部署和操作，而最新技术则依赖于离线和在线级别的建模，传感和控制的各个阶段中支持学习的组​​件。本文解决了嵌入神经网络组件的动态系统的运行时安全监视问题。开发了间隔观察器形式的运行时安全状态估计器，以构造运行时系统状态轨迹的下限和上限。所开发的运行时安全状态估计器由两个嵌入到动态系统中的神经网络派生的辅助神经网络组成，观察者获得的收益可确保其积极性，即估计器在运行时约束系统状态的能力，以及相应误差动态的收敛。设计程序是根据一系列线性规划可行性问题制定的。通过数值示例说明了所开发的方法，并通过对自适应巡航控制系统的评估对其进行了验证。