A bounded-error approach to piecewise affine system identification
A bounded-error approach to piecewise affine system identification
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DOI：
10.1109/tac.2005.856667
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发表时间：
2005-10
影响因子：
6.8
通讯作者：
A. Bemporad;A. Garulli;S. Paoletti;A. Vicino
中科院分区：
文献类型：
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作者：
A. Bemporad;A. Garulli;S. Paoletti;A. Vicino
本文提出了分段仿射自回归外生(PWARX)模型的三阶段参数辨识方法。第一阶段同时对数据点进行分类，并估计子模型的数量和相应的参数，方法是将数据分解为一组合适的线性互补不等式的最小可行子系统(Min PFS)问题。其次，改进程序减少了误分类并改进了参数估计。第三阶段通过两类或多类线性分离技术确定回归集的多面体划分。作为一个主要特征，该算法要求识别误差有界于一个量/SPL增量/。这样的界限是在拟合质量和模型复杂性之间权衡的一个有用的调整参数。通过数值算例和电子元器件贴装过程的实验数据验证了所提出的PWA系统辨识方法的有效性。
This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.