Data-driven identification of vehicle dynamics using Koopman operator
Data-driven identification of vehicle dynamics using Koopman operator
复制标题
使用 Koopman 算子进行数据驱动的车辆动力学识别
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Hromčík
中科院分区：
文献类型：
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作者：
Vít Cibulka;T. Haniš;M. Hromčík
本文介绍了使用库普曼算子识别车辆动力学的结果。基本思想是使用所谓的基函数将非线性系统（在我们的例子中是汽车）的状态空间转换为高维空间，其中系统动力学是线性的。基函数的选择至关重要，并且对于如何选择它们没有通用的方法，本文对此进行了一些讨论。提出了两种不同的选择基函数的方法。第一种方法基于扩展动态模式分解，严重依赖专家基础选择，并且完全由数据驱动。第二种方法利用非线性动力学知识，用于构造库普曼算子的本征函数，根据定义，该本征函数沿着非线性系统轨迹线性演化。然后将特征函数用作预测的基函数。每种方法都提供了数值示例，并讨论了该方法对于非线性车辆系统的可行性。
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis functions, where the system dynamics is linear. The selection of basis functions is crucial and there is no general approach on how to select them, this paper gives some discussion on this topic. Two distinct approaches for selecting the basis functions are presented. The first approach, based on Extended Dynamic Mode Decomposition, relies heavily on expert basis selection and is completely data-driven. The second approach utilizes the knowledge of the nonlinear dynamics, which is used to construct eigenfunctions of the Koopman operator which are known by definition to evolve linearly along the nonlinear system trajectory. The eigenfunctions are then used as basis functions for prediction. Each approach is presented with a numerical example and discussion on the feasibility of the approach for a nonlinear vehicle system.