基于高斯混合聚类的切换系统的辨识

针对具有未知切换规则与未知子系统数量的切换系统的辨识问题,提出一种两阶段辨识方法,包括模式检测与参数辨识.在模式检测阶段,首先建立高斯混合模型表示采样数据的分布,并通过轮盘法选择合适的初始模型参数.其次,计算采样数据属于每个子系统的后验概率,通过极大似然估计算法迭代更新模型参数,使高斯混合模型最大化地拟合采样数据的分布.在此基础上,通过贝叶斯信息准则确定子系统的数量,并根据最大后验概率准则估计切换规则.在参数辨识阶段,通过递推增广最小二乘法估计每个子系统的参数向量.最后,通过仿真结果验证了所提方法的有效性.

Identification of switched systems based on Gaussian mixture clustering

In order to solve the identification problem of switched systems with unknown switched rules and unknownnumber of subsystems, a two-stage identification method is proposed, including mode detection and parameter identification.In the mode detection stage, the Gaussian mixture model is first established to represent the distribution of sampleddata, and appropriate initial model parameters are selected according to the roulette method. Secondly, the posterior probabilityof the sampled data belong to each subsystem is calculated, and the maximum likelihood estimation algorithm is usedto iteratively update the model parameters to make the Gaussian mixture model maximum fit the distribution of the sampleddata. On this basis, the number of subsystems is determined by the Bayesian information criterion, and the switched ruleis estimated according to the maximum a posteriori criterion. In the parameter identification stage, the parameter vectorof each subsystem is estimated by the recursive extended least square method. Finally, the effectiveness of the proposedmethod is verified according to simulation results.