Learning Deep Input-Output Stable Dynamics

• URL: http://arxiv.org/abs/2206.13093v1
• Date: Mon, 27 Jun 2022 07:54:34 GMT
• Title: Learning Deep Input-Output Stable Dynamics
• Authors: Yuji Okamoto and Ryosuke Kojima
• Abstract summary: 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. Results show that the nonlinear system with neural networks by our method achieves the input-output stability, unlike naive neural networks.
• Score: 2.055949720959582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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