Learning Deep Input-Output Stable Dynamics
This work addresses stability in robotics and physical modeling, offering an incremental improvement for ensuring robustness in learned systems.
The authors tackled the problem of learning stable dynamics from time-series data by proposing a method to guarantee input-output stability in nonlinear systems, achieving stability in neural networks where naive approaches failed.
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.