Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control
arxiv(2023)
摘要
In this work, we aim to analyze 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 also applied
to provide novel sample complexity and regret guarantees for nominal
receding-horizon LQ controllers in a learning-based setting.
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