Piecewise smooth system identification in reproducing kernel Hilbert space
Piecewise smooth system identification in reproducing kernel Hilbert space
复制标题
再生核希尔伯特空间中的分段光滑系统辨识
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
G. Bloch
中科院分区：
文献类型：
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作者：
Fabien Lauer;G. Bloch
本文将Ohlsson和Ljung最近提出的分段仿射系统辨识方法推广到非线性情况，同时从聚类的角度出发。在这种方法中，问题被铸造作为凸成本函数的最小化，实现了对数据的拟合和稀疏性之前的数量之间的权衡。在这里，我们认为分段光滑系统识别的非线性情况下，没有先验知识的类型所涉及的非线性。这是通过同时学习的局部模型的集合，从再生核希尔伯特空间通过凸泛函的最小化，我们证明了一个表示定理，提供了明确的形式的解决方案。一个应用于分段光滑系统辨识的例子表明，该方法能准确地估计出系统的模态和非线性局部模型。
The paper extends the recent approach of Ohlsson and Ljung for piecewise affine system identification to the nonlinear case while taking a clustering point of view. In this approach, the problem is cast as the minimization of a convex cost function implementing a trade-off between the fit to the data and a sparsity prior on the number of pieces. Here, we consider the nonlinear case of piecewise smooth system identification without prior knowledge on the type of nonlinearities involved. This is tackled by simultaneously learning a collection of local models from a reproducing kernel Hilbert space via the minimization of a convex functional, for which we prove a representer theorem that provides the explicit form of the solution. An example of application to piecewise smooth system identification shows that both the mode and the nonlinear local models can be accurately estimated.