Neural Stochastic Contraction Metrics for Learning-based Control and Estimation
Abstract
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
© 2021 AACC. This work was funded in part by the Raytheon Company and benefited from discussions with Nicholas Boffi and Quang-Cuong Pham.Additional details
- Eprint ID
- 110417
- Resolver ID
- CaltechAUTHORS:20210825-150704832
- Raytheon Company
- Created
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2021-08-25Created from EPrint's datestamp field
- Updated
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2021-08-25Created from EPrint's last_modified field
- Caltech groups
- GALCIT, Center for Autonomous Systems and Technologies (CAST)