Reduced-Size Kernel Models for Nonlinear Hybrid System Identification
Reduced-Size Kernel Models for Nonlinear Hybrid System Identification
复制标题
用于非线性混合系统辨识的缩小尺寸核模型
DOI：
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发表时间：
2011
影响因子：
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通讯作者：
Fabien Lauer
中科院分区：
文献类型：
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作者：
Van Luong Le;G. Bloch;Fabien Lauer
这篇简短的论文着重于识别非线性混合动力学系统，即在多种非线性动力学行为之间切换的系统。因此，目的是从回归设置中的一组输入输出数据中学习一个子模型集合，而没有对数据点分组为相似行为的事先了解。为了能够近似任意的非线性，考虑了内核子模型。但是，为了在将方法应用于大数据集时保持效率，为了固定子模型尺寸并限制优化变量的数量，就需要进行预处理步骤。这篇简短的论文提出了四种方法，分别受固定尺寸最小二乘支持向量机的启发子模型。这些在数值实验中进行了比较，这些实验表明所提出的方法可以同时以有效，准确的方式对数据点进行分类和非线性行为的近似。
This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.