Learning Deep Input-Output Stable Dynamics

Ryosuke Kojima · Yuji Okamoto

Hall J #402

Keywords: [ Dynamical Systems ] [ Nonlinear system identification ] [ Input-output stability ]

[ Abstract ]
[ Paper [ Poster [ OpenReview
Tue 29 Nov 2 p.m. PST — 4 p.m. PST


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 .

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