论文标题
克服尺寸的诅咒，以近似于在小细胞状态下具有深层神经网络的近似值函数
Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition
论文作者
论文摘要
我们提出了一个深层神经网络体系结构，用于存储普通微分方程系统的近似Lyapunov函数。在系统上的小增益条件下，具有固定准确性的Lyapunov函数所需的神经元数仅在状态维度上增长，即，所建议的方法能够克服维度的诅咒。
We propose a deep neural network architecture for storing approximate Lyapunov functions of systems of ordinary differential equations. Under a small-gain condition on the system, the number of neurons needed for an approximation of a Lyapunov function with fixed accuracy grows only polynomially in the state dimension, i.e., the proposed approach is able to overcome the curse of dimensionality.
