A Transfer Learning Method for Safety Control of Linear Systems under Input Saturation

While the safe reinforcement learning (RL) control has been addressed in several studies, achieving safety during the training phase remains a significant challenge. Training directly in hazardous environments through trial and error inherently leads to unsafe behaviors. To address this, we propose a novel safety-certified transfer learning method for linear systems, where an RL controller is first trained to stabilize the system in a risk-free environment and then transferred to the hazardous environment. The primary challenge is to ensure that, after the transfer, the learning-based controller can guarantee safety while preserving stability. To this end, differential geometry tools are employed to analyze the geometric relationship between the systems before and after transfer and design the transferred controller accordingly. Theoretical analysis proves that the transferred controller can stabilize the system and enforce its safety, as long as the original RL controller stabilizes the system. Moreover, the proposed transfer method imposes saturation constraints on the transferred controller to prevent invalid control inputs that may arise from controller modification after transfer. The conditions for the existence of the transferred controller are derived. Finally, the effectiveness of the proposed method is demonstrated by a vehicle control case study.