Smart Predict-Then-Control: Control-Aware Surrogate Refinement for System Identification

This paper introduces Smart Predict Then Control (SPC), a control aware refinement procedure for model based control. SPC refines a prediction oriented model by optimizing a surrogate objective that evaluates candidate models through the control actions they induce. For a fixed surrogate variant under unconstrained control, we establish the smoothness of the surrogate, projected gradient convergence at a sublinear rate of order one over K, and a bias decomposition that yields a conditional transfer diagnostic. On a wind disturbed quadrotor trajectory tracking task, Updated SPC reduces tracking RMSE by 70 percent and closed loop cost by 42 percent relative to the nominal baseline.