Short-term dependency of a class of nonlinear continuous time dynamic systems
Short-term dependency of a class of nonlinear continuous time dynamic systems
复制标题
一类非线性连续时间动态系统的短期依赖性
DOI：
10.1016/j.engappai.2021.104402
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发表时间：
2021
影响因子：
8
通讯作者：
Li, Lichun
中科院分区：
文献类型：
--
作者：
Sun, Jieming;Li, Lichun
动态系统通常具有长期依赖性。然而，最近的研究表明，像递归神经网络这样的长期记忆模型和像前馈神经网络这样的短期记忆模型在近似动态系统的行为方面具有相当的性能。当先驱研究者试图理解离散时间动态系统中的短期依赖性时，本文重点研究了一类由常微分方程表征的连续时间动态系统。在这类连续时间动态系统中，只能观测到变量，不能直接测量其对时间的导数。通过分析连续时间动态系统和采样系统的可观测性，证明了在快速采样时，当前输出仅依赖于有限步的历史信息。如果采样足够快，使得欧拉近似可以很好地近似采样系统，则当前输出仅依赖于最近n步的历史信息。这里，n是常微分方程的阶数。随后，我们用NARMAX方法验证了我们的结果。
Dynamic systems usually have long-term dependency. Recent work, however, shows that the long-term memory models like recurrent neural networks and short-term memory models like feed-forward neural networks have comparable performance in approximating the behavior of dynamic systems. While the pioneering researchers try to understand the short-term dependency in discrete time dynamic systems, this paper focuses on a class of continuous time dynamic systems characterized by ordinary differential equations. In this class of continuous time dynamic systems, only the variable can be observed, and its derivatives with respect to time cannot be measured directly. By analyzing the observability of the continuous time dynamic systems and the sampled systems, we show that the current output only depends on finite steps of history information when sampling fast. If the sampling is fast enough such that the Euler approximation can approximate the sampled system well, the current output only relies on the most recent n steps of history information. Here, n is the order of the ordinary differential equation. Later, we verified our results with the NARMAX method.