Chance Constrained Model Predictive Control via Active Uncertainty Set Learning and Calibration

Model predictive control (MPC) under chance constraints has been a promising solution to complicated control problems subject to uncertain disturbance. However, traditional approaches either require exact knowledge of probabilistic distributions, or rely on massive multi-scenarios that are generated to represent uncertainties. In this paper, a novel approach is proposed based on actively learning a compact high-density region from available data in form of a polytope. This is achieved by adopting the support vector clustering, which has been recently utilized in data-driven robust optimization. A new strategy is developed to calibrate the size of the polytope, which provides appropriate probabilistic guarantee. Finally the optimal control problem is cast as a robust optimization problem, which can be efficiently handled by existing numerical solvers. The proposed method commonly requires less data samples than traditional approaches, and can help reducing the conservatism, thereby enhancing the practicability of model predictive control. The efficacy of the proposed method is verified based on a simulated example.