论文标题
通过混合界限对神经反馈系统的可及性分析和安全验证
Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopes
论文作者
论文摘要
通过引入其他二进制变量并具有一些独特的属性，可以使它们方便地表示非convex集，从而概括了受约束的分区。本文介绍了基于新型混合生物学的方法，用于神经反馈系统的可及性分析和安全验证。提出了算法来计算前馈神经网络每一层的输入输出关系，以及神经反馈系统的确切可触及集。此外，将足够且必要的条件作为混合企业线性程序制定，以证明神经反馈系统的轨迹是否可以避免不安全的区域。所提出的方法显示出一种制定的配方，为神经反馈系统的可触及集提供了最紧密的凸松弛。开发了可达集的复杂性降低技术，以平衡计算效率和近似精度。两个数值示例表明，与其他现有方法相比，所提出的方法的出色表现。
Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods for the reachability analysis and safety verification of neural feedback systems. Algorithms are proposed to compute the input-output relationship of each layer of a feedforward neural network, as well as the exact reachable sets of neural feedback systems. In addition, a sufficient and necessary condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions. The proposed approach is shown to yield a formulation that provides the tightest convex relaxation for the reachable sets of the neural feedback system. Complexity reduction techniques for the reachable sets are developed to balance the computation efficiency and approximation accuracy. Two numerical examples demonstrate the superior performance of the proposed approach compared to other existing methods.
