Well-Specified Control Cost Decay

Background: Controllers derived from data-driven predictors are evaluated based on the infinite-horizon LQR cost of the resulting closed-loop system. In a well-specified setting, the faster decay of prediction error for the single-step predictor should translate to better control performance decay.

Question / Future Work: Compare the rate of decay of the infinite-horizon LQR cost for controllers trained using single-step vs. intermediate predictors, especially analyzing the dependency on the prediction horizon $H$ and whether the single-step predictor’s superior prediction error decay rate translates to a faster decay in closed-loop control performance.