Almost Surely Stable Deep Dynamics
arXiv:2103.14722
Abstract
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications such as estimation and control. However, these aspects exacerbate the challenge of guaranteeing stability. Our method works by embedding a Lyapunov neural network into the dynamic model, thereby inherently satisfying the stability criterion. To this end, we propose two approaches and apply them in both the deterministic and stochastic settings: one exploits convexity of the Lyapunov function, while the other enforces stability through an implicit output layer. We demonstrate the utility of each approach through numerical examples.
arXiv commentNeurIPS 2020; Spotlight Paper
References in corpus (14)
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Weight Uncertainty in Neural Networks
- Safe Model-based Reinforcement Learning with Stability Guarantees
- Deep Equilibrium Models
- Input Convex Neural Networks
- Differentiable Convex Optimization Layers
- Neural Lyapunov Control
- Stable Recurrent Models
- Lyapunov Theory for Discrete Time Systems
- The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems
- Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation
- Stability of Gaussian Process State Space Models
- Modify the Improved Euler scheme to integrate stochastic differential equations
- Neural Networks with Cheap Differential Operators