Clustering of Linear Time-Invariant Systems: A Bayesian Nonparametric Method

Abstract

In this paper, we consider the clustering of linear time-invariant (LTI) systems according to the similarity of dynamics. There are two main difficulties for clustering of LTI systems: one is to determine the labels of LTI systems and the number of clusters, and another one is to build models of LTI systems. To address these two difficulties simultaneously, a Bayesian nonparametric method based on Dirichlet process mixture models (DPMM) and kernel-based regularization method is proposed. To be specific, the Dirichlet process mixtures of Bayesian linear regression models (DPM-BLRM) is proposed to determine the label of each LTI system according to the probability that the system belongs to each cluster, and adapt the number of clusters to the complexity of data. In addition, DPM-BLRM incorporates the prior knowledge of LTI systems to deal with the possible large variance of model parameters estimation when the collected data is short or has low signal-to-noise ratio, where the carrier of prior knowledge is kernel matrix. Then Markov chain Monte Carlo (MCMC) method is used for Bayesian inference for the DPM-BLRM. The simulation results illustrate the efficiency of the proposed method.