Distributionally Robust Model Predictive Control: Closed-Loop Guarantees and Scalable Algorithms

• 成果类型: Article
• 署名作者: McAllister, Robert D.; Esfahani, Peyman Mohajerin
• 署名单位: Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3498702
• 发表日期: 2025
• 页码: 2963-2978
• 关键词: costs; Closed loop systems; uncertainty; trajectory; Stochastic processes; Predictive control; Prediction algorithms; Robustness; optimal control; cost function; Closed-loop stability; distributionally robust optimization (DRO); model predictive control (MPC); second-order algorithms

摘要

We establish a collection of closed-loop guarantees and propose a scalable optimization algorithm for distributionally robust model predictive control (DRMPC) applied to linear systems, convex constraints, and quadratic costs. Via standard assumptions for the terminal cost and constraint, we establish distributionally robust long-term and stagewise performance guarantees for the closed-loop system. We further demonstrate that a common choice of the terminal cost, i.e., via the discrete-algebraic Riccati equation, renders the origin input-to-state stable for the closed-loop system. This choice also ensures that the exact long-term performance of the closed-loop system is independent of the choice of ambiguity set for the DRMPC formulation. Thus, we establish conditions under which DRMPC does not provide a long-term performance benefit relative to stochastic MPC. To solve the DRMPC optimization problem, we propose a Newton-type algorithm that empirically achieves superlinear convergence and guarantees the feasibility of each iterate. We demonstrate the implications of the closed-loop guarantees and the scalability of the proposed algorithm via two examples. To facilitate the reproducibility of the results, we also provide open-source code to implement the proposed algorithm and generate the figures.