Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

Lantao Xie; Lei Xie; Hongye Su; Jingdai Wang

doi:10.1109/JAS.2018.7511126

Volume 5 Issue 4

Jul. 2018

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2018 > 5(4): 765-770

Lantao Xie, Lei Xie, Hongye Su and Jingdai Wang, "Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 765-770, July 2018. doi: 10.1109/JAS.2018.7511126

Citation:

Lantao Xie, Lei Xie, Hongye Su and Jingdai Wang, "Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 765-770, July 2018. doi: 10.1109/JAS.2018.7511126

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Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

doi: 10.1109/JAS.2018.7511126

Lantao Xie^1
,,
Lei Xie^1
,,
Hongye Su^{1
,
,},
Jingdai Wang^2
,

1.
State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China
2.
College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China

Funds:

the Natural Science Foundation of Zhejiang Province LR17F030002

the Science Fund for Creative Research Groups of the National Natural Science Foundation of China 61621002

More Information

Author Bio:
Lantao Xie received the B.S. degree in 2009 from Zhejiang University, China and is currently a Ph.D. candidate in the College of Control Science and Engineering, Zhejiang University. His research interests include model predictive control and machine learning. (e-mail: lantao@zju.edu.cn)

Lei Xie received the B.S. degree in 2000 and the Ph.D. degree in 2005 from Zhejiang University, China. Between 2005 and 2006, he was a postdoctoral researcher at Berlin University of Technology, an Assistant Professor between 2005 and 2008 and is currently a Professor at the College of Control Science and Engineering, Zhejiang University. His research interests include control performance assessment, statistical process monitoring and fault diagnosis, and process modeling and advanced control. (e-mail: leix@iipc.zju.edu.cn)

Hongye Su (SM'10) received the B.S. degree in industrial automation from Nanjing University of Chemical Technology, China, in 1990, and the M.S. and Ph.D. degrees from Zhejiang University, China, in 1993 and 1995, respectively. From 1995 to 1997, he was a Lecturer with the Department of Chemical Engineering, Zhejiang University, where he was then promoted to an Associate Professor with the Institute of Advanced Process Control from 1998 to 2000. He is currently a Professor with the Institute of Cyber-Systems and Control, Zhejiang University. His current research interests include robust controls, time-delay systems, and advanced process control theory and applications. (e-mail: hysu@iipc.zju.edu.cn)

Jingdai Wang graduated from Zhejiang University in 1996 and received the M.S. and Ph.D. degrees from Zhejiang University in 1999 and 2002 respectively. He is currently a Professor with the College of Chemical and Biological Engineering, Zhejiang University, and the director of Zhejiang Provincial Key Laboratory of Chemical Efficient Manufacturing Technology. He is a fixed researcher of the State Key Laboratory of Chemical Engineering, winner of the National Outstanding Youth Fund, young and middle-aged leader in science and technology innovation. His research interests include polymerization reaction project, multiphase flow reaction engineering, multiphase flow detection and information processing research, etc. (e-mail: wangjd@zju.edu.cn)
Corresponding author: Hongye Su, e-mail: hysu@iipc.zju.edu.cn
Received Date: 2018-01-19
Accepted Date: 2018-04-13

Abstract

Abstract

Feasible sets play an important role in model predictive control (MPC) optimal control problems (OCPs). This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron (represented by linear matrix inequalities) and polyhedral (represented by a set of inequalities) constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices, the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.
- Feasible set computation,
- linear matrix inequalities (LMIs),
- model predictive control (MPC),
- polyhedron

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References(27)

References

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Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

doi: 10.1109/JAS.2018.7511126

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