Learning Deep Input-Output Stable Dynamics-猫眼课题宝

DOI：

10.48550/arxiv.2206.13093

发表时间：

2022-06

期刊：

ArXiv

影响因子：

通讯作者：

中科院分区：

其他

文献类型：

作者：

Yuji Okamoto;Ryosuke Kojima

从观测的时间序列数据中学习稳定的动力学是机器人、物理建模和系统生物学中的一个基本问题。这些动态中的许多被表示为与外部环境通信的输入-输出系统。在这项研究中，我们专注于输入输出稳定的系统，表现出对意外的刺激和噪声的鲁棒性。我们提出了一种方法来学习非线性系统，保证输入输出稳定性。我们提出的方法利用可微投影到满足Hamilton-Jacobi不等式的空间来实现输入输出稳定性。找到这个投影的问题可以制定为一个二次约束二次规划问题，我们推导出特定的解决方案解析。此外，我们将我们的方法应用于玩具模型和训练从葡萄糖-胰岛素模拟器生成的基准的任务。结果表明，与朴素神经网络相比，该方法使非线性系统具有输入输出稳定性。我们的代码可以在https://github.com/clinfo/DeepIOStability上找到。

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.

Learning Deep Input-Output Stable Dynamics

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