Learning Stable Deep Dynamics Models
By J. Kolter, Gaurav Manek. 2020
246 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics
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Citations in the corpus
- Equivariant Flows: exact likelihood generative learning for symmetric densities (2020, methodology): “Here we foresee combining our results either with symplectic integrators or by restricting the class of dynamics functions to those which are numerically stable e.g. as done in (Manek & Kolter, 2020).”
- Safe Control With Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control (2022, background): “This approach provides the foundation for many certificatebased learning works; early examples include [47], and later works include [3], [48], [49], [50], [51], [52], [53], and [54].”
- On the Sample Complexity of Stability Constrained Imitation Learning (2021, methodology): “Although this may be computationally challenging, alternating optimization schemes have been proposed and successfully applied in other contexts, see for example [16, 31–33].”