Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency

This paper proposes a multistage suboptimal model predictive control (MPC) strategy which can reduce the prediction horizon without compromising the stability property. The proposed multistage MPC requires a precomputed sequence of j-step admissible sets, where the j-step admissible set is the set of system states that can be steered to the maximum positively invariant set in j control steps. Given the precomputed admissible sets, multistage MPC first determines the minimum number of steps M required to drive the state to the terminal set. Then, it steers the state to the (M - N)-step admissible set if M>N, or to the terminal set otherwise. The paper presents the offline computation of the admissible sets, and shows the feasibility and stability of multistage MPC for systems with and without disturbances. A numerical example illustrates that multistage MPC with N=5 can be used to stabilize a system which requires MPC with N >= 14 in the absence of disturbances, and requires MPC with N >= 22 when affected by disturbances.