Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control
This work provides theoretical guarantees for learning-based control, offering sample complexity and regret bounds that can improve controller design in applications like robotics or autonomous systems.
The paper analyzes how modeling error, terminal value function error, and prediction horizon affect the performance of a receding-horizon linear quadratic controller, finding that optimal horizons can be one or infinity depending on error differences and that finite horizons near controllability indices achieve near-optimal performance.
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.