Stabilization of nonlinear systems using stepwise moving horizon control with contractive constraints

In this paper, a new algorithm for the control of discrete-time non-linear systems is presented. This new strategy may be interpreted as a solution combining the Receding Horizon method and the Intervalwise Moving Horizon Control with Contractive Constraints. The former strategy is used as a theoretical aid for guaranteing the existence of solutions to the minimization procedures. For this reason, the conditions that the system must comply to ensure stabilization are of Contractive Constraint type. The algorithm proposed involves one minimization procedure for each lag of the control sequence, leading to a potentially better disturbance rejection behavior when compared with Intervalwise Moving Horizon Control methods.