2023/01/19 by Shengling Shi, Shi, Shengling, Anastasios Tsiamis +3
Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #Advanced Control Systems Optimization #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2301.07876
openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
This work analyzes how the trade-off 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 one or infinity 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.