Almost Surely Stable Deep Dynamics
This addresses stability issues in dynamic models for applications like estimation and control, but appears incremental as it builds on existing Lyapunov-based methods.
The paper tackles the challenge of learning provably stable deep neural network dynamic models from observed data, particularly in discrete-time stochastic settings, by embedding a Lyapunov neural network to inherently satisfy stability criteria, and demonstrates utility through numerical examples.
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.