Learning Stable Deep Dynamics Models
This addresses the challenge of ensuring reliable, formally verifiable behavior in deep learning-based control and prediction systems, which is incremental but important for safety-critical applications.
The paper tackles the problem of making formal stability guarantees for deep neural network models of dynamical systems, achieving this by jointly learning a dynamics model with a Lyapunov function that ensures stability across the entire state space.
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been difficult to make formal claims about the basic properties of the learned systems. In this paper, we propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. The approach works by jointly learning a dynamics model and Lyapunov function that guarantees non-expansiveness of the dynamics under the learned Lyapunov function. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics, such as video textures, in a fully end-to-end fashion.