基于模糊聚类的PWA系统的模型辨识

针对一类分段仿射结构的离散时间混杂系统，其模型辨识可等价成对系统数据的分类、分类边界的优化及分类数据的线性回归问题.利用改进的G-K 模糊聚类算法，克服聚类迭代过程出现的非数值解问题；以综合性能指标最优确定最佳的子模型个数，从而获得最佳的分类数据; 以隶属度为权值，采用加权最小二乘算法提高子模型辨识精度；通过聚类中心最短法则确定两两相邻的子数据集，利用支持向量机思想，构造出一个标准的二次规划问题，得到凸多面体的方程系数. 仿真结果验证了该方法的有效性和实用性.

Model Identification of Piecewise Affine (PWA) Systems Based on Fuzzy Cluster

For a class of discrete-time hybrid system in the piecewise affine form, its model identification problem is equivalent to the problems of classification of the cluster data of the system, the optimized classification of boundary and linear regression. Using improved G-K fuzzy cluster algorithm to solve the numerical problems in iterated processes, the optimal cluster data can be obtained. The number of sub-models can be estimated from multi-performance indexes. In each cluster, the parameters of sub-model are obtained by the weighted least squares method. Two adjacent regions were achieved with the nearest distance among the cluster centers. The boundary hyper-plane can be estimated by using a soft margin support vector machine. Simulation results show good performances of this effective technique.