Beyond Inherent Robustness: Strong Stability of MPC Despite Plant-Model Mismatch

• 成果类型: Article
• 署名作者: Kuntz, Steven J.; Rawlings, James B.
• 署名单位: University of California System; University of California Santa Barbara; University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3604662
• 发表日期: 2026
• 关键词: Predictive control; asymptotic stability; margins; systems; gain; tool

摘要

In this article, we establish the asymptotic stability of model predictive control (MPC) under plant-model mismatch for problems where the origin remains a steady state despite mismatch. This class of problems includes, but is not limited to, inventory management, path planning, and control of systems in deviation variables. Our results differ from prior results on the inherent robustness of MPC, which guarantee only convergence to a neighborhood of the origin, the size of which scales with the magnitude of the mismatch. For MPC with quadratic costs, continuous differentiability of the system dynamics is sufficient to demonstrate exponential stability of the closed-loop system despite mismatch. For MPC with general costs, a joint comparison function bound and scaling condition guarantee asymptotic stability despite mismatch. The results are illustrated in numerical simulations, including the classic upright pendulum problem. The tools developed to establish these results can address the stability of offset-free MPC, an open and interesting question in the MPC research literature.