Dictionary-free Koopman model predictive control with nonlinear input transformation

The paper proves KMPC convexity and derives a condensed quadratic program by stacking predictions (Y = MV + Cz) and input-increment relations (ΔV = DV + Cv), yielding a QP min V^T F V + q^T V with linear box constraints; the candidate solution performs the same elimination but chooses ΔV as the decision variable and uses the cumulative-sum map, arriving at the identical convex QP structure. Differences are only representational (V vs ΔV, D vs cumulative L), not substantive.