  In this paper, model predictive control (MPC) strategies are proposed for
dead-beat control of linear systems with and without state and control
constraints. In unconstrained MPC, deadbeat performance can be guaranteed by
setting the control horizon to the system dimension, and adding an terminal
equality constraint. It is proved that the unconstrained deadbeat MPC is
equivalent to linear deadbeat control. The proposed constrained deadbeat MPC is
designed by setting the control horizon equal to the system dimension and
penalizing only the terminal cost. The recursive feasibility and deadbeat
performance are proved theoretically.
