A Partial Approximate Least Absolute Deviation-Based Identification Algorithm for a Multivariable Closed-Loop System with Spike Noise

Abstract

Considering the stability and safety of industrial production, the open-loop system cannot meet the requirements of industrial production, so more and more attention has been paid to multivariable closed-loop system identification. This study focuses on the identification of a multivariate closed-loop system with spike noise in which the model order of the feedback channel is lower than that of the forward channel. Combining principal component analysis (PCA), which is used to eliminate the correlation between the data matrix elements, and the derivable approximate least absolute criterion function, partial approximate least absolute deviation (PALAD) for multivariable closed-loop system identification is proposed. By introducing a deterministic function to replace the absolute value in partial approximate least absolute deviation, the non-differentiable problem of the least absolute deviation function can be solved, and the identifiability of the multivariable closed-loop system in the case mentioned above is theoretically verified. Simulation experiments show the validity of the PALAD algorithm. Compared with the partial least squares (PLS) method, PALAD can effectively restrain the spike noise that follows an SαS distribution and shows stronger robustness when white and spike noises exist simultaneously.