Maximal terminal region approach for MPC using subsets sequence

doi:10.1007/s11460-012-0178-y

Front Elect Electr Eng

2012, Vol. 7

Issue (2) : 270-278 https://doi.org/10.1007/s11460-012-0178-y

RESEARCH ARTICLE

Maximal terminal region approach for MPC using subsets sequence

Yafeng WANG^1,2, Fuchun SUN¹(

), Huaping LIU¹, Dongfang YANG¹

1. Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China; 2. The Aviation General Office in Guangzhou Bureau of Naval General Armaments Department, Anshun 561018, China

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Abstract

For the sake of enlarging the domain of attraction of model predictive control (MPC), a novel approach of gradually approximating the maximal terminal state region is proposed in this paper. Given the terminal cost, both surrounding set sequence and subsets sequence of the maximal terminal region were constructed by employing one-step set expansion iteratively. It was theoretically proved that when the iteration time goes to infinity, both the surrounding set sequence and the subsets sequence will converge to the maximal terminal region. All surrounding and subsets sets in these sequences are extracted from the state space by exploiting support vector machine (SVM) classifier. Finally, simulations are implemented to validate the effectiveness of this approach.

Keywords model predictive control (MPC) terminal region domain of attraction support vector machine (SVM)

Corresponding Author(s): SUN Fuchun,Email:fcsun@mail.tsinghua.edu.cn

Issue Date: 05 June 2012

Cite this article:

Yafeng WANG,Fuchun SUN,Huaping LIU, et al. Maximal terminal region approach for MPC using subsets sequence[J]. Front Elect Electr Eng, 2012, 7(2): 270-278.

URL:

https://academic.hep.com.cn/fee/EN/10.1007/s11460-012-0178-y
https://academic.hep.com.cn/fee/EN/Y2012/V7/I2/270

Fig.1 Approximating process of surrounding set sequence

Fig.2 Approximating process of subsets sequence

Fig.3 Approximation process of surrounding set sequence

Fig.4 Approximation process of subsets sequence

Fig.5 Closed-loop trajectories of states

1	Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M. Constrained model predictive control: Stability and optimality. Automatica , 2000, 36(6): 789-814 doi: 10.1016/S0005-1098(99)00214-9
2	González A H, Odloak D. Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance. Automatica , 2009, 45(4): 1080-1085 doi: 10.1016/j.automatica.2008.11.015
3	Magni L, De Nicolao G, Magnani L, Scattolini R. A stabilizing model based predictive control algorithm for nonlinear systems. Automatica , 2001, 37(9): 1351-1362
4	Chen H, Allgower F. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica , 1998, 34(10): 1205-1217 doi: 10.1016/S0005-1098(98)00073-9
5	Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytopic invariant sets. Automatica , 2003, 39(8): 1487-1494 doi: 10.1016/S0005-1098(03)00128-6
6	De Doná J A, Seron M M, Mayne D Q, Goodwin G C. Enlarged terminal sets guaranteeing stability of receding horizon control. Systems & Control Letters , 2002, 47(1): 57-63 doi: 10.1016/S0167-6911(02)00175-5
7	Ong C J, Sui D, Gilbert E G. Enlarging the terminal region of nonlinear model predictive control using the support vector machine method. Automatica , 2006, 42(6): 1011-1016 doi: 10.1016/j.automatica.2006.02.023
8	Limon D, Alamo T, Salas F, Camacho E F. On the stability of constrained MPC without terminal constraint. IEEE Transactions on Automatic Control , 2006, 51(5): 832-836 doi: 10.1109/TAC.2006.875014
9	Limon D, Alamo T, Camacho E F. Enlarging the domain of attraction of MPC controllers. Automatica , 2005, 41(4): 629-635 doi: 10.1016/j.automatica.2004.10.011
10	Burges C C. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery , 1998, 2(2): 121-167 doi: 10.1023/A:1009715923555
11	Vapnik V. The Nature of Statistical Learning Theory. New York: Springer, 1995
12	Wang Y F, Sun F C, Zhang Y A, Liu H P, Min H B. Getting a suitable terminal cost and maximizing the terminal region for MPC. Mathematical Problems in Engineering, 2010 , 2010: 1-16

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