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.

翻译：过度使用可达的动态系统组群是安全核查和稳健控制合成中的一个基本问题。 这些组群的表示是影响计算复杂性和近似误差的一个关键因素。 在本文中,我们开发了一种新办法,利用适应性模板多面板来过度使用可达的神经网络动态系统组群。我们使用线性层的单值分解以及激活功能的形状来调整每个时段的多面形的几何与真实可达数据集的几何测量值。我们然后提出一个分支和限制方法,以计算推断模板对可达的组群的准确过量。我们说明了拟议方法在对由神经网络控制器驱动的线性系统进行可达性分析时的效用。