Certainty-Equivalence Model Predictive Control: Stability, Performance, and Beyond

• 成果类型: Article
• 署名作者: Liu, Changrui; Shi, Shengling; De Schutter, Bart
• 署名单位: Delft University of Technology; Massachusetts Institute of Technology (MIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3661789
• 发表日期: 2026
• 关键词: exponential decay; nonlinear MPC; state; feasibility; sensitivity

摘要

Handling model mismatch is a common challenge in model predictive control (MPC). While robust MPC is effective, its conservatism often makes it less desirable. Certainty-equivalence MPC (CE-MPC), which uses the nominal model, offers an appealing alternative due to its design simplicity and low computational cost. This article investigates CE-MPC for uncertain nonlinear systems with multiplicative parametric uncertainty and input constraints that are inactive at the steady state. The primary contributions are twofold. First, a novel perturbation analysis of the MPC value function is provided, without assuming the Lipschitz continuity of the stage cost, better tailored to the widely used quadratic costs, and having broader applicability in value function approximation, learning-based MPC, and performance-driven MPC design. Second, the stability and performance analysis of CE-MPC is provided, quantifying the suboptimality of CE-MPC compared to the infinite-horizon optimal controller with perfect model knowledge. The results provide insights into how the prediction horizon and model mismatch jointly affect stability and the worst-case performance. Furthermore, the general results are specialized to linear quadratic control, and a competitive-ratio bound is derived, serving as the first competitive-ratio bound for MPC of uncertain linear systems with input constraints and multiplicative uncertainty.