Q-Learning Control for LPV Systems Based on Influence Function and Predictive Safety Filter Correction Feedback

To address the problems of inferior-quality data and excessive PSF post-corrections in practical LPV safety control, this paper proposes a safe Q-learning control method integrated with influence function and PSF correction feedback. First, an influence function is introduced to quantify the impact of individual samples on Q-function updates. By evaluating the variation in loss functions before and after removing each sample, samples with adverse effects on policy updates are identified and eliminated so as to mitigate the negative impacts of low-quality data on Q-function estimation and controller updating. Second, the PSF correction term is incorporated into the cost function as a penalty to guide the learning of nominal control actions with reduced reliance on PSF intervention. In summary, the proposed method improves the nominal control policy from two perspectives: learning-data cleaning and safety-correction feedback. While optimizing LPV system performance and reducing PSF correction times, it still guarantees the satisfaction of system safety constraints. Simulation results show that the proposed method can effectively improve learning-data quality, reduce PSF corrections, and ensure the safety and stability of the closed-loop system. The turbofan engine case study further demonstrates that the proposed method can achieve stable regulation while satisfying the prescribed safety constraints, verifying its applicability to practical LPV systems.