In this paper, we consider the problem of training neural network (NN) controllers for cyber-physical systems (CPS) that are guaranteed to satisfy safety and liveness properties. Our approach is to combine model-based design methodologies for dynamical systems with data-driven approaches to achieve this target. Given a mathematical model of the dynamical system, we compute a finite-state abstract model that captures the closed-loop behavior under all possible neural network controllers. Using this finite-state abstract model, our framework identifies the subset of NN weights that are guaranteed to satisfy the safety requirements. During training, we augment the learning algorithm with a NN weight projection operator that enforces the resulting NN to be provably safe. To account for the liveness properties, the proposed framework uses the finite-state abstract model to identify candidate NN weights that may satisfy the liveness properties. Using such candidate NN weights, the proposed framework biases the NN training to achieve the liveness specification. Achieving the guarantees above, can not be ensured without correctness guarantees on the NN architecture, which controls the NN's expressiveness. Therefore, and as a corner step in the proposed framework is the ability to select provably correct NN architectures automatically.

中文翻译：

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使用可达性分析可正确校正神经网络控制器的训练

在本文中，我们考虑为网络物理系统（CPS）训练神经网络（NN）控制器的问题，该控制器可保证满足安全性和活动性。我们的方法是将基于模型的动态系统设计方法与数据驱动方法相结合，以实现这一目标。给定动力学系统的数学模型，我们计算一个有限状态抽象模型，该模型捕获所有可能的神经网络控制器下的闭环行为。使用此有限状态抽象模型，我们的框架可以确定可以保证满足安全要求的NN权重的子集。在训练期间，我们使用NN权重投影运算符增强了学习算法，该运算符强制生成的NN证明是安全的。为了说明活动属性，提出的框架使用有限状态抽象模型来识别可以满足活跃性的候选NN权重。使用这样的候选NN权重，所提出的框架使NN训练偏向于达到活度规范。如果没有控制NN表现力的NN体系结构的正确性保证，就无法实现上述保证。因此，作为所提出框架中的关键步骤，是能够自动选择可证明正确的NN体系结构。它控制了神经网络的表达能力。因此，作为所提出框架中的关键步骤，是能够自动选择可证明正确的NN体系结构。它控制了神经网络的表达能力。因此，作为所提出框架中的关键步骤，是能够自动选择可证明正确的NN体系结构。