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.
Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 14, 2013; final manuscript received December 24, 2013; published online March 11, 2014. Assoc. Editor: Bryan Rasmussen.
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Liu, X., Constantinescu, D., and Shi, Y. (March 11, 2014). "Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency." ASME. J. Dyn. Sys., Meas., Control. May 2014; 136(3): 031026. https://doi.org/10.1115/1.4026413
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