Data-Driven Plant–Model Mismatch Detection for Closed-Loop LPV System Based on Instrumental Variable Using Sum-of-Norms Regularization

Models are the key to model-based control strategies. However, due to the nonlinear and time-varying nature of industrial processes, plant–model mismatches are inevitable. Therefore, it is highly desirable to detect mismatches and update the model in a closed-loop system to avoid re-identifying the entire model. In this study, a mismatch detection method based on the instrumental variable that uses sum-of-norms regularization and is robust to noise modeling errors is proposed for linear parameter variation-input–output (IO) models. The introduction of the instrumental variable addresses the challenge that regression variables are corrupted with colored noise. The proposed method integrates the detection and quantification of mismatches into a framework in which significant jumps in parameters can be detected by segmenting the signal using sum-of-norms regularization and the search space of quantification is reduced. Moreover, the method is noninvasive and applicable to closed-loop systems under colored noise disturbances. Finally, the feasibility and robustness of the proposed method under closed-loop conditions are analyzed from a stochastic perspective and demonstrated with representative simulation examples.