A sparse low-rank matrix recovery strategy to deal with robust identification for multi-model systems with time-varying delays

Abstract

A robust identification problem for multi-model systems with time-vary delays is considered in this article, where the linear parameter varying model is employed to present the structure of the multi-model systems. To handle outliers in the collected data, we establish an observation model based on a robust principal component analysis (RPCA) algorithm for low-rank matrix recovery. Construct a high-dimensional information matrix using multi-batch measured data. Although this matrix is typically high-dimensional and low-rank, outliers cause it to become high-dimensional and high-rank. By applying the RPCA algorithm, we restore the information matrix to its low-rank form, thus isolating the pure collected data. This process allows us to select a batch of collected data as information vectors for parameter identification. A Markov chain model is established to describe the correlation between time delays. Given the complexity of optimizing log-likelihood functions directly, we derive the estimation problem of model parameters and time delays under the framework of the expectation maximization (EM) algorithm. Therefore, an EM identification algorithm based on RPCA (RPCA-EM) is derived. A numerical simulation and an example involving a continuous stirred tank reactor verify the effectiveness of the proposed RPCA-EM algorithm.