Neural Stochastic Contraction Metrics for Learning-Based Control and Estimation

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