We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The NSCM framework allows autonomous agents to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic neural contraction metric, as illustrated in simulation results.

中文翻译：

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基于学习的鲁棒控制和估计的神经随机收缩指标

我们提出了神经随机收缩度量（NSCM），这是一种用于一类随机非线性系统可证明稳定的鲁棒控制和估计的新设计框架。它使用频谱归一化的深度神经网络来构造收缩指标，该指标通过随机设置中的简化凸优化进行采样。频谱归一化将度量的状态导数约束为Lipschitz连续，从而确保在随机扰动下系统轨迹的均方距离的指数有界。NSCM框架允许自治主体实时近似最优的稳定控制和估计策略，并且优于现有的非线性控制和估计技术，包括依赖于状态的Riccati方程，迭代LQR，EKF和确定性神经收缩度量，