An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

Peng-Yuan Zheng; Yu-Geng Xi; De-Wei Li

doi:10.1007/s11633-010-0565-x

February 2011

Article Contents

Peng-Yuan Zheng, Yu-Geng Xi and De-Wei Li. An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations. International Journal of Automation and Computing, vol. 8, no. 1, pp. 134-140, 2011. doi: 10.1007/s11633-010-0565-x

Cite as: Peng-Yuan Zheng, Yu-Geng Xi and De-Wei Li. An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations. International Journal of Automation and Computing, vol. 8, no. 1, pp. 134-140, 2011. doi: 10.1007/s11633-010-0565-x

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

Peng-Yuan Zheng^{1,2
,
,},
Yu-Geng Xi^1,2,
De-Wei Li^1,2

1.
Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PRC;
2.
Key Laboratory of System Control and Information Processing, Ministry of Education, PRC

Author Biography:

Yu-Geng Xi received the Dr.-Ing.de- gree in automatic control from the Techni- cal University Munich,Germany in 1984.
Corresponding author: Peng-Yuan Zheng received his B.Sc. degree in electrical engineering and au- tomation from the North University of China,PRC in 2000,the M.Sc.

Received: 2010-04-13

Fund Project:

supported by National Natural Science Foundation of China (No.60934007, No.61074060);China Postdoctoral Science Foundation (No.20090460627);Shanghai Postdoctoral Scientific Program (No.10R21414600);China Postdoctoral Science Foundation Special Support (No.201003272)

Abstract

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

References

[1]	X.B.Hu,W.H.Chen.A modified model predictive control scheme.International Journal of Automation and Comput- ing,vol.2,no.1,pp.101-106,2005.
[2]	X.B.Hu,W.H.Chen.Model predictive control of non- linear systems:Stability region and feasible initial control. International Journal of Automation and Computing,vol.4, no.2,pp.195-202,2007.
[3]	M.V.Kothare,V.Balakrishnan,M.Morari.Robust con- strained model predictive control using linear matrix in- equalities.Automatica,vol.32,no.10,pp.1361-1379,1996.
[4]	Z.Y.Wan,M.V.Kothare.An e?cient o?-line formula- tion of robust model predictive control using linear matrix inequalities.Automatica,vol.39,no.5,pp.837-846,2003.
[5]	Z.Y.Wan,M.V.Kothare.E?cient robust constrained model predictive control with a time varying terminal con- straint set.Systems and Control Letters,vol.48,no.5, pp.375-383,2003.
[6]	B.Pluymers,J.A.K.Suykens,B.D.Moor.Min-max feed- back MPC using a time-varying terminal constraint set and comments on e?cient robust constrained model predictive control with a time-varying terminal constraint set.Systems and Control Letters,vol.54,no.12,pp.1143-1148,2005.
[7]	Z.Y.Wan,B.Pluymers,M.V.Kothare,B.D.Moor.Com- ments on:E?cient robust constrained model predictive control with a time varying terminal constraint set by Wan and Kothare.Systems and Control Letters,vol.55,no.7, pp.618-621,2006.
[8]	D.Angeli,A.Casavola,E.Mosca.Ellipsoidal low- demanding MPC schemes for uncertain polytopic discrete- time systems.In Proceedings of the 41st IEEE Conference on Decision and Control,IEEE,Las Vegas,USA,vol.3, pp.2935-2940,2002.
[9]	M.T.Cychowski,B.C.Ding,H.Tang,T.O Mahony.A new approach to o?-line constrained robust model predic- tive control.In Proceedings of the UK Control Conference, Las Vegas,USA,pp.146-151,2004.
[10]	Y.I.Lee,B.Kouvaritakis.Constrained robust model pre- dictive control based on periodic invariance.Automatica, vol.42,no.12,pp.2175-2181,2006.
[11]	D.W.Li,Y.G.Xi.Design of robust model predictive control based on multi-step control set.Acta Automatica Sinica,vol.35,no.4,pp.433-437,2009.
[12]	D.W.Li,Y.G.Xi,P.Y.Zheng.Constrained robust feedback model predictive control for uncertain systems with polytopic description.International Journal of control, vol.82,no.7,pp.1267-1274,2009.
[13]	F.Wu.LMI-based robust model predictive control and its application to an industrial CSTR problem.Journal of Pro- cess Control,vol.11,no.6,pp.649-659,2001.
[14]	D.Q.Mayne,J.B.Rawlings,C.V.Rao,P.O.M.Scokaert. Constrained model predictive control:Stability and opti- mality.Automatica,vol.36,no.6,pp.789-814,2000.
[15]	P.Gahinet,A.Nemirovski,A.J.Laub,M.Chilali.LMI Control Toolbox:For Use with MATLAB,Natick,USA: The Mathworks,1995.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

1. Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PRC;

2. Key Laboratory of System Control and Information Processing, Ministry of Education, PRC

Corresponding author: Peng-Yuan Zheng received his B.Sc. degree in electrical engineering and au- tomation from the North University of China,PRC in 2000,the M.Sc.

Received: 2010-04-13

Fund Project:

Key words:

Abstract: In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

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Reference (15)

[1]	X.B.Hu,W.H.Chen.A modified model predictive control scheme.International Journal of Automation and Comput- ing,vol.2,no.1,pp.101-106,2005.
[2]	X.B.Hu,W.H.Chen.Model predictive control of non- linear systems:Stability region and feasible initial control. International Journal of Automation and Computing,vol.4, no.2,pp.195-202,2007.
[3]	M.V.Kothare,V.Balakrishnan,M.Morari.Robust con- strained model predictive control using linear matrix in- equalities.Automatica,vol.32,no.10,pp.1361-1379,1996.
[4]	Z.Y.Wan,M.V.Kothare.An e?cient o?-line formula- tion of robust model predictive control using linear matrix inequalities.Automatica,vol.39,no.5,pp.837-846,2003.
[5]	Z.Y.Wan,M.V.Kothare.E?cient robust constrained model predictive control with a time varying terminal con- straint set.Systems and Control Letters,vol.48,no.5, pp.375-383,2003.
[6]	B.Pluymers,J.A.K.Suykens,B.D.Moor.Min-max feed- back MPC using a time-varying terminal constraint set and comments on e?cient robust constrained model predictive control with a time-varying terminal constraint set.Systems and Control Letters,vol.54,no.12,pp.1143-1148,2005.
[7]	Z.Y.Wan,B.Pluymers,M.V.Kothare,B.D.Moor.Com- ments on:E?cient robust constrained model predictive control with a time varying terminal constraint set by Wan and Kothare.Systems and Control Letters,vol.55,no.7, pp.618-621,2006.
[8]	D.Angeli,A.Casavola,E.Mosca.Ellipsoidal low- demanding MPC schemes for uncertain polytopic discrete- time systems.In Proceedings of the 41st IEEE Conference on Decision and Control,IEEE,Las Vegas,USA,vol.3, pp.2935-2940,2002.
[9]	M.T.Cychowski,B.C.Ding,H.Tang,T.O Mahony.A new approach to o?-line constrained robust model predic- tive control.In Proceedings of the UK Control Conference, Las Vegas,USA,pp.146-151,2004.
[10]	Y.I.Lee,B.Kouvaritakis.Constrained robust model pre- dictive control based on periodic invariance.Automatica, vol.42,no.12,pp.2175-2181,2006.
[11]	D.W.Li,Y.G.Xi.Design of robust model predictive control based on multi-step control set.Acta Automatica Sinica,vol.35,no.4,pp.433-437,2009.
[12]	D.W.Li,Y.G.Xi,P.Y.Zheng.Constrained robust feedback model predictive control for uncertain systems with polytopic description.International Journal of control, vol.82,no.7,pp.1267-1274,2009.
[13]	F.Wu.LMI-based robust model predictive control and its application to an industrial CSTR problem.Journal of Pro- cess Control,vol.11,no.6,pp.649-659,2001.
[14]	D.Q.Mayne,J.B.Rawlings,C.V.Rao,P.O.M.Scokaert. Constrained model predictive control:Stability and opti- mality.Automatica,vol.36,no.6,pp.789-814,2000.
[15]	P.Gahinet,A.Nemirovski,A.J.Laub,M.Chilali.LMI Control Toolbox:For Use with MATLAB,Natick,USA: The Mathworks,1995.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

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