A stable block model predictive control with variable implementation horizon

In this paper, we present a stable model predictive control method for discrete-time nonlinear systems. The standard MPC scheme is modified to incorporate (1) a block implementation scheme where a sub-string of the optimized input sequence is applied instead of a single value; (2) an additional constraint which guarantees that a Lyapunov function will decrease over time; (3) a variable implementation window that facilitates the stability constraint enforcement. Stability of the closed-loop system with the proposed algorithm is established. Examples 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.