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For a receding-horizon controller with a known system and with an approximateterminal value function, it is well-known that increasing the predictionhorizon can improve its control performance. However, when the prediction modelis inexact, a larger prediction horizon also causes propagation andaccumulation of the prediction error. In this work, we aim to analyze theeffect of the above trade-off between the modeling error, the terminal valuefunction error, and the prediction horizon on the performance of a nominalreceding-horizon linear quadratic (LQ) controller. By developing a novelperturbation result of the Riccati difference equation, a performance upperbound is obtained and suggests that for many cases, the prediction horizonshould be either 1 or infinity to improve the control performance, depending onthe relative difference between the modeling error and the terminal valuefunction error. The obtained suboptimality performance bound is also applied toprovide end-to-end performance guarantees, e.g., regret bounds, for nominalreceding-horizon LQ controllers in a learning-based setting.

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