A stable block model predictive control with variable implementation horizon

In this paper, we present a stable receding horizon model predictive control for discrete-time nonlinear systems. The standard MPC scheme is modified to incorporate (1) a block implementation scheme where a string of the optimized input is applied instead of a single value; (2) an additional constraint which guarantees that a Lyapunov function decreases over time; (3) a variable implementation window that facilitates the constraints enforcement. Stability of the closed-loop system with the proposed algorithm is established. Examples and simulation results are given to illustrate the effectiveness of the control scheme. The impacts of several key design parameters on the overall performance are also analyzed and discussed.