Learning-Based Model Predictive Control With High-Probability Safety Using Gaussian Mixture Models

This article introduces a learning-based model predictive control (MPC) framework that leverages Gaussian mixture models (GMMs) to address dynamic system uncertainties effectively. To address the limitations of traditional MPC methods in handling system disturbances and uncertainties, we integrate GMM into the MPC framework to model and account for these disturbances probabilistically. By reformulating the chance constraints within this framework, the proposed approach provides high-probability safety guarantees. Specifically, GMM can capture complex disturbance distributions in dynamic systems compared with traditional Gaussian processes, thereby enabling more precise prediction and optimization within the MPC loop. This ensures that the resulting control strategies not only satisfy safety constraints but also enhance system performance. Experimental evaluations demonstrate that the proposed method achieves superior performance in satisfying high-probability safety requirements while enhancing the overall robustness of the system. Compared to conventional MPC approaches, the proposed method can effectively tackle the challenges posed by uncertainties, ensuring stability and safety under diverse conditions. This approach has broad applications in domains that require robust control under uncertainties, including autonomous driving, robotic manipulation, and other complex engineering systems.