Distributionally Robust Stochastic MPC under Disturbance-Affine Feedback Policies
For control engineers dealing with uncertain systems, this work offers a less conservative MPC approach that improves performance while maintaining recursive feasibility and stability.
This paper proposes a distributionally robust stochastic MPC framework using disturbance-affine feedback policies, which outperforms tube-based MPC in terms of initial feasible sets, average performance, and state variance control.
This study addresses the stochastic Model Predictive Control (MPC) problem for linear time-invariant systems subjected to unknown disturbance distributions. By leveraging the most recent disturbance data, we construct a set of distributions with similar statistical properties contained within a Wasserstein ball, thereby accounting for the worst-case impacts on constraint satisfaction. Numerous MPC strategies, particularly tube-based approaches, have been extensively studied under the Wasserstein ambiguity set, but these methods often introduce conservatism and can limit control performance. Unlike tube-based approaches, we adopt a disturbance-affine control strategy, which introduces additional control degrees of freedom. We begin by developing the Disturbance-Affine Distributionally Robust (DA-DR) MPC framework, subsequently reformulating the control problem into a tractable quadratic programming formulation. Furthermore, we establish the recursive feasibility and stability of the proposed MPC scheme. Finally, we present comprehensive theoretical analysis and simulation results, demonstrating the superiority of the DA-DR MPC over tube-based MPC in initial feasible sets, average performance, and state variance control.