Suboptimality Analysis of Receding-Horizon Quadratic Control With Unknown Linear Systems and Its Applications in Learning-Based Control

• 成果类型: Article
• 署名作者: Shi, Shengling; Tsiamis, Anastasios; De Schutter, Bart
• 署名单位: Massachusetts Institute of Technology (MIT); Delft University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3605539
• 发表日期: 2026
• 关键词: model-predictive control

摘要

This work analyzes how the tradeoff between the modeling error, the terminal value function error, and the prediction horizon affects the performance of a nominal receding-horizon linear quadratic (LQ) controller. By developing a novel perturbation result of the Riccati difference equation, a novel performance upper bound is obtained and suggests that for many cases, the prediction horizon can be either 1 or $+\infty$ to improve the control performance, depending on the relative difference between the modeling error and the terminal value function error. The result also shows that when an infinite horizon is desired, a finite prediction horizon that is larger than the controllability index can be sufficient for achieving a near-optimal performance, revealing a close relation between the prediction horizon and controllability. The obtained suboptimality performance upper bound is applied to provide novel sample complexity and regret guarantees for nominal receding-horizon LQ controllers in a learning-based setting. We show that an adaptive prediction horizon that increases as a logarithmic function of time is beneficial for regret minimization.