Learning stable dynamics from observed time-series data is an essential
problem in robotics, physical modeling, and systems biology. Many of these
dynamics are represented as an inputs-output system to communicate with the
external environment. In this study, we focus on input-output stable systems,
exhibiting robustness against unexpected stimuli and noise. We propose a method
to learn nonlinear systems guaranteeing the input-output stability. Our
proposed method utilizes the differentiable projection onto the space
satisfying the Hamilton-Jacobi inequality to realize the input-output
stability. The problem of finding this projection can be formulated as a
quadratic constraint quadratic programming problem, and we derive the
particular solution analytically. Also, we apply our method to a toy bistable
model and the task of training a benchmark generated from a glucose-insulin
simulator. The results show that the nonlinear system with neural networks by
our method achieves the input-output stability, unlike naive neural networks.
Our code is available at https://github.com/clinfo/DeepIOStability.Comment: Accepted in NeurIPS 202