Learning Stability Certificates from Data

Abstract

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error - the probability that a certificate will not certify a new, unseen trajectory - when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.

Fixes an error in the statement and proof of Theorem 5.1, Theorem 5.2, and Proposition D.1

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• Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction
• On the Sample Complexity of Stability Constrained Imitation Learning
• Efficient Learning of a Linear Dynamical System with Stability Guarantees
• Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers
• Memory-Efficient Learning of Stable Linear Dynamical Systems for Prediction and Control
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks
• Adaptive Variants of Optimal Feedback Policies
• Learn Proportional Derivative Controllable Latent Space from Pixels