Regret Analysis of Online LQ Control Using Trajectory Prediction and Tracking

• 成果类型: Article
• 署名作者: Chen, Yitian; Molloy, Timothy L.; Summers, Tyler; Shames, Iman
• 署名单位: Australian National University; University of Texas System; University of Texas Dallas; University of Melbourne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3641253
• 发表日期: 2026

摘要

We propose a new framework for solving online linear quadratic (LQ) control problems with time-varying cost matrices that are known only up to the current time or over a short preview window. Our framework involves using revealed cost matrices to predict the unknown optimal trajectory, and then using a tracking controller to drive the system toward this prediction. We adopted the notion of dynamic regret to measure and bound the resulting quality of control decisions with and without system disturbances, and present a constructive tracking controller design approach based on deadbeat control in a lifted space. Our analysis reveals that the regret of controllers designed using this proposed framework is upper bounded by terms that decay exponentially with the number of time steps over which future cost matrices can be previewed. Our simulations show that our proposed framework leads to controllers with improved performance compared to previously proposed online LQ methods that do not use revealed cost matrices. The exponential decay of dynamic regret with respect to the preview window length present in our regret bounds is also observed in simulations.