Neural Stochastic Contraction Metrics for Learning-based Control and Estimation
This addresses the challenge of real-time stable control and estimation for autonomous agents in stochastic environments, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackles the problem of provably-stable robust control and estimation for stochastic nonlinear systems by introducing Neural Stochastic Contraction Metrics (NSCM), which uses a spectrally-normalized deep neural network to construct a contraction metric, resulting in outperformance over existing techniques like state-dependent Riccati equation and EKF in simulations.
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.