The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.

中文翻译：

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分段仿射系统的带位参数识别

本文研究了如何识别分段仿射系统的问题，其中所考虑的分段仿射系统是一个特殊的非线性系统。之所以不容易识别这种分段仿射系统，是因为每个分离区域和每个未知参数向量都需要同时确定。然后，首先，为了实现识别目标，提出了多类分类过程来确定每个分离的区域。由于提出的多类分类过程与经典数据聚类策略相同，多类分类过程可以结合凸优化的一阶算法，同时实现分类过程的目标。其次，利用区位参数识别算法构造一个集合，其中包含未知参数向量。在这种带位参数识别算法中，放宽了对外部噪声的严格概率描述，并对每个未知参数向量进行了识别。此外，这个构造的集合与测量的输出和对应于噪声的给定界限一致。第三，关于保证我们的衍生区位不会随着迭代无限增长的充分条件被表述为显式线性矩阵不等式。最后，通过仿真算例证明了该带位环参数识别算法的有效性。这个构造的集合与测量的输出和对应于噪声的给定界限一致。第三，关于保证我们的衍生区位不会随着迭代无限增长的充分条件被表述为显式线性矩阵不等式。最后，通过仿真算例证明了该带位环参数识别算法的有效性。这个构造的集合与测量的输出和对应于噪声的给定界限一致。第三，保证我们的衍生区位不会随着迭代无限增长的充分条件被表述为显式线性矩阵不等式。最后，通过仿真算例证明了该带位环参数识别算法的有效性。