Distributional Uncertainty and Model Predictive Control
Robert D. McAllister
Delft Center for Systems and Control, Delft University of Technology
Tuesday, November 21, 2023, 11:00
Advances in distributionally robust optimization (DRO) have inspired a range of distributionally robust model predictive control (DRMPC) formulations. These DRMPC formulations consider the worst-case probability distribution for the disturbance within some ambiguity set and implement this solution via the standard rolling horizon framework of MPC, thereby generalizing stochastic MPC (SMPC) and robust MPC (RMPC) formulations. While these new formulations are interesting, there remain important questions about the efficacy of including yet another layer of uncertainty in the MPC problem. The main focus of this talk is provide greater insight into these questions, i.e., is DRMPC worth it? Specifically, I will present recent results on the inherent distributionally robustness of (nonlinear) stochastic MPC and then introduce a DRMPC formulation for linear systems and quadratic costs with provable closed-loop properties. For this DRMPC formulation, I will further demonstrate conditions under which DRMPC does *not* provide a long-term performance benefit relative to SMPC. To solve these DRMPC problems, I will present a tailored newton-type algorithm that achieves a 50% reduction in computation time compared to solving the DRMPC problem as a semi-definite program via MOSEK. I will conclude with a small example to demonstrate these insights and the performance of the proposed algorithm.