论文标题
解开控制膜系统的可解释推理的漂移和控制矢量场
Disentangling Drift- and Control- Vector Fields for Interpretable Inference of Control-affine Systems
论文作者
论文摘要
许多工程以及自然发生的动态系统没有精确的数学模型来描述其动态行为。但是，在许多应用程序中，可以使用外部输入探测系统并测量过程变量，从而产生丰富的数据存储库。使用时间序数据来推断描述基本动力学过程的数学模型是一个重要且具有挑战性的问题。在这项工作中，我们提出了一个模型重建程序，用于推断受输入仿射结构控制的一类非线性系统的动力学。特别是，我们提出了一个数据生成和学习策略，以使与漂移和控制媒介领域相关的重建问题解析，并能够量化其对系统动力学的各自贡献。该学习过程导致了一种可解释和可靠的模型推断方法。我们提出了几个数值示例，以证明所提出方法的功效和灵活性。
Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and measure the process variables, resulting in abundant data repositories. Using the time-series data to infer a mathematical model that describes the underlying dynamical process is an important and challenging problem. In this work, we propose a model reconstruction procedure for inferring the dynamics of a class of nonlinear systems governed by an input affine structure. In particular, we propose a data generation and learning strategy to decouple the reconstruction problem associated with the drift- and control- vector fields, and enable quantification of their respective contributions to the dynamics of the system. This learning procedure leads to an interpretable and reliable model inference approach. We present several numerical examples to demonstrate the efficacy and flexibility of the proposed method.
