论文标题
学习深入输入输出稳定动力学
Learning Deep Input-Output Stable Dynamics
论文作者
论文摘要
从观察到的时间序列数据中学习稳定的动力学是机器人技术，物理建模和系统生物学中的重要问题。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，我们专注于投入输出稳定系统，表现出对意外刺激和噪声的鲁棒性。我们提出了一种学习保证输入输出稳定性的非线性系统的方法。我们提出的方法利用了满足汉密尔顿 - 雅各比不平等的空间上的可区分投影来实现输入输出稳定性。找到该投影的问题可以作为二次约束二次编程问题进行配合，我们通过分析得出特定的解决方案。此外，我们将方法应用于玩具双基型模型以及训练由葡萄糖 - 胰岛素模拟器产生的基准测试的任务。结果表明，通过我们的方法，具有神经网络的非线性系统可以达到输入输出稳定性，这与天真的神经网络不同。我们的代码可在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.
