Neural Stochastic Contraction Metrics for Learning-based Control and Estimation

TL;DR

This paper introduces Neural Stochastic Contraction Metrics (NSCM), a neural network-based method for designing provably stable and robust control and estimation strategies for stochastic nonlinear systems, enabling real-time autonomous decision-making.

Contribution

The paper proposes a novel NSCM framework that combines spectral normalization and convex optimization to ensure stability and robustness in stochastic control and estimation.

Findings

Outperforms existing control methods like iLQR and Riccati equations.

Ensures exponential boundedness of system trajectories under stochastic disturbances.

Enables real-time approximation of optimal control and estimation policies.

Abstract

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.