论文标题
通过自适应多面体对神经网络控制系统的自动达到性分析
Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes
论文作者
论文摘要
过度考虑到达动力学系统的可触及集合是安全验证和鲁棒控制合成中的一个基本问题。这些集合的表示是影响计算复杂性和近似误差的关键因素。在本文中，我们开发了一种新的方法，用于过度使用自适应模板多面体对可触及的神经网络动力学系统的可触及集。我们使用线性层的奇异值分解以及激活函数的形状，以使每个时间步骤的多型的几何形状适应真实可及的集合的几何形状。然后，我们提出了一种分支和结合方法，以计算由推断模板对可触及的集合进行准确的过度评估。我们说明了拟议方法在神经网络控制器驱动的线性系统的可及性分析中的实用性。
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers.
