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Published November 2021 | public
Journal Article Open

Neural Stochastic Contraction Metrics for Learning-based Control and Estimation


We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, 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 trained NSCM model allows autonomous systems 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 NCM, as shown in simulation results.

Additional Information

© 2020 IEEE. Manuscript received September 14, 2020; revised November 18, 2020; accepted December 7, 2020. Date of publication December 22, 2020; date of current version January 13, 2021. This work was supported in part by the Raytheon Company. This work was benefited from discussions with Nicholas Boffi and Quang-Cuong Pham. Code: https://github.com/astrohiro/nscm.

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August 20, 2023
September 8, 2023