Nonlinear Spatio-Temporal Run-to-Run Control: Leveraging Diffusion Models for Disturbance Management

Run-to-run (R2R) control is widely used in advanced manufacturing. Conventional R2R control methods often assume that system disturbances exhibit linear structures or low-rank approximations in high-dimensional data, such as images or videos. While these assumptions facilitate implementation, they limit the effectiveness of R2R control in managing sophisticated manufacturing processes with intricate nonlinear disturbances. To address these challenges, we propose a novel nonlinear spatio-temporal R2R control framework that estimates system disturbances using a diffusion model and applies control actions to compensate for them. The proposed approach integrates an offline modeling phase to capture disturbance dynamics and an online control phase that dynamically adjusts control actions to minimize deviations from the target system response. Unlike conventional deterministic control strategies, the proposed method explicitly quantifies uncertainty, enabling more robust and informed decision-making. The effectiveness of this method is validated through simulation studies and a case study, demonstrating its adaptability in complex, high-dimensional environments.