LS-SVM for LPV-ARX Identification: Efficient Online Update by Low-Rank Matrix Approximation

Least-Squares Support Vector Machine (LS-SVM) is a promising approach to data-driven identification of Linear Parameter-Varying (LPV) models. As for other data-driven methods, the performance of the LS-SVM model identification method is strictly related to data available off-line for training the algorithm. Further, this method does not consider the possibility to learn from on-line data, or at least this is not possible in a computationally efficient way. These aspects limit the possibility to exploit the features of the algorithm in real-world applications. This paper presents an online updating procedure of LPV-ARX (AutoRegressive with eXogenous input) model based on the Low-Rank (LR) matrix approximation aided to overcome these limits. The proposed method permits to improve the base of knowledge of the provided LS-SVM by introducing the possibility to learn from on-line data, neglecting to perform the time-expensive training phase, such that the proposed approach is suitable for on-line execution. In order to further limit the computational cost and the storage memory related to the on-line learning feature, the proposed approach permits to maintain the original algorithm requirements by introducing a forgetting method able to neglect less important data. The performance of the proposed solution has been evaluate considering as case study a Spark-Ignited (SI) aircraft engine system identification.