Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control

• URL: http://arxiv.org/abs/2301.07876v3
• Date: Mon, 16 Dec 2024 19:24:22 GMT
• Title: Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control
• Authors: Shengling Shi, Anastasios Tsiamis, Bart De Schutter,
• Abstract summary: We show that for many cases, the prediction horizon can be either one or infinity to improve the control performance. We show that an adaptive prediction horizon that increases as a logarithmic function of time is beneficial for regret minimization.
• Score: 14.279848166377668
• License:
• Abstract: 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 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.

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