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Research Papers

Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency

[+] Author and Article Information
Xiaotao Liu

Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055,
STN CSC,
Victoria, BC V8W 3P6, Canada
e-mail: xtliu@uvic.ca

Daniela Constantinescu

Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055,
STN CSC,
Victoria, BC V8W 3P6, Canada
e-mail: danielac@uvic.ca

Yang Shi

Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055,
STN CSC,
Victoria, BC V8W 3P6, Canada
e-mail: yshi@uvic.ca

1Corresponding author.

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.

J. Dyn. Sys., Meas., Control 136(3), 031026 (Mar 11, 2014) (8 pages) Paper No: DS-13-1319; doi: 10.1115/1.4026413 History: Received August 14, 2013; Revised December 24, 2013

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 (MN)-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.

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Figures

Grahic Jump Location
Fig. 1

The initial state x(0), the maximum positively invariant set Xfm and the admissible sets I5,I8,I14 for the mini-hovercraft without disturbances

Grahic Jump Location
Fig. 2

State evolution of mini-hovercraft without disturbances and controlled using: multistage MPC with N = 5; multistage MPC with N = 8; and conventional MPC with N = 14

Grahic Jump Location
Fig. 3

Control action of mini-hovercraft without disturbances and controlled using: multistage MPC with N = 5; multistage MPC with N = 8; and conventional MPC with N = 14

Grahic Jump Location
Fig. 4

The initial state x(0), the maximum robust positively invariant set Sf and the admissible sets I5,I8,I22 for the nominal mini-hovercraft with tightened constraints

Grahic Jump Location
Fig. 5

State evolution of the mini-hovercraft with disturbances and controlled using: multistage robust MPC with N = 5; multistage robust MPC with N = 8; and robust MPC with fixed horizon N = 22

Grahic Jump Location
Fig. 6

Control action for the mini-hovercraft with disturbances

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