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.

翻译：我们提出了神经物理分解仪(NSCM),这是对一类随机非线性系统进行可靠稳健控制和估算的新设计框架,它使用光谱标准化的深神经网络来构建一个收缩度尺,通过在随机环境中的简化锥形优化进行取样。 光谱正常化制约了该测量的状态-衍生物为Lipschitz的连续性,从而确保了系统轨迹在随机干扰下的平均平方距离的指数界限。 NSCM框架允许自主物剂在实时中近似最佳稳定控制和估算政策,并超越了现有的非线性控制和估算技术,包括州独立的里卡提方程式、迭代LQR、EKF和确定性神经收缩度指标,如模拟结果所说明的那样。