基于自适应多面体的神经网络控制系统可达性自动化分析
Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes
AI总结：
本文提出了一种利用自适应模板多面体过近似神经网络动态系统可达集的新方法，通过线性层奇异值分解和激活函数形状调整多面体几何形状，并采用分支定界方法计算精确过近似，提升了可达性分析的准确性。
摘要：
过近似动态系统的可达集是安全验证和鲁棒控制综合中的一个基本问题。这些集合的表示是影响计算复杂度和近似误差的关键因素。本文开发了一种使用自适应模板多面体来过近似神经网络动态系统可达集的新方法。我们利用线性层的奇异值分解以及激活函数的形状，在每个时间步将多面体的几何形状调整为与真实可达集的几何形状相匹配。然后，我们提出了一种分支定界方法，通过推断的模板计算可达集的准确过近似。我们在线性系统由神经网络控制器驱动的可达性分析中展示了所提方法的实用性。
英文摘要：
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.
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