Multistage Model Predictive Control based on Data-Driven Distributionally Robust Optimization

In this article, a novel distributionally robust optimization (DRO) based multistage model predictive control (MPC) framework is proposed to hedge against the uncertainty in control problems. Without a priori knowledge of the exact uncertainty distribution, an ambiguity set, constructed based on principal component analysis, incorporates the first-order moment information instead. A linear performance measure is chosen so that the worst-case expected problem can be exactly dualized by adopting the affine decision rule. By considering input and state constraints robustly with respect to a support set, which specifies the domain of the uncertainty, the DRO-based MPC model is developed as a robust optimization problem. The proposed framework is illustrated on a two-mass-spring system and results show the improved control performance compared to traditional control strategies.