Abstract
This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.
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M. L. Darby and M. Nikolaou, “MPC: Current practice and challenges,” Control Engineering Practice, vol. 20, no. (4), pp. 328–342, April 2012.
S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, vol. 7, no. (11), pp.733–764, July 2003.
A. Kumara and Z. Ahmada, “Model predictive control (MPC) and its current issues in Chemical Engineering,” Chemical Engineering Communications, vol. 199, no. (4), pp. 472–511, 2012.
P. Bumroongsri and S. Kheawhom, “Robust model predictive control with time–varying tubes,” International Journal of Control, Automation and Systems, vol. 15, no. (4), pp. 1479–1484, August 2017.
D. Q. Mayne, “Model predictive control: recent developments and future promise,” Automatica, vol. 50, no. (12), pp. 2967–2986, December 2014.
R. Zhang, D. Chen, and X. Ma, “Nonlinear predictive control of a hydropower system model,” Entropy, vol. 17, no. (9), pp. 6129–6149, September 2015.
M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. (10), pp. 1361–1379, October 1996.
H. S. Abbas, N. Meskin, J. Mohammadpour, and J. Hanema, “An MPC approach for LPV systems in inputoutput form,” Proceedings of the 54th IEEE Conference on Decision and Control, pp. 91–96, Osaka, Japan, December 2015.
W. Yang, J. Gao, G. Feng, and T. Zhang, “An optimal approach to output–feedback robust model predictive control of LPV systems with disturbances,” International Journal of Robust and Nonlinear Control, vol. 26, no. (15), pp. 3253–3273, October 2016.
D. He, H. Huang, and Q. Chen, “Quasi–min–max MPC for constrained nonlinear systems with guaranteed input–tostate stability,” Journal of the Franklin Institute, vol. 351, no. (6), pp. 3405–3423, June 2014.
Y. Lu and Y. Arkun, “Quasi–min–max MPC algorithms for LPV systems,” Automatica, vol. 36, no. (4), pp. 527–540, April 2000.
Y. I. Lee and B. Kouvaritakis, “Constrained robust model predictive control based on periodic invariance,” Automatica, vol. 42, no. (12), pp. 2175–2181, December 2006.
D. Li and Y. Xi, “The Feedback Robust MPC for LPV Systems with bounded rates of parameter changes,” IEEE Transactions on Automatic Control, vol. 55, no. (2), pp. 503–507, February 2010.
P. Zheng, D. Li, Y. Xi, and J. Zhang, “Improved model prediction and RMPC design for LPV systems with bounded parameter changes,” Automatica, vol. 49, no. (12), pp. 3695–3699, December 2013.
P. Zheng, D. Li, Y. Xi, and X. Li, “A sophisticated RMPC design for LPV systems based on the mixed multi–step feedback control,” Proceedings of the 34th Chinese Control Conference, pp. 4119–4123, Hangzhou, China, July 2015.
X. Ping, Z. Li, and P. Wang, “Dynamic output feedback robust MPC for LPV systems subject to input saturation and bounded disturbance,” International Journal of Control, Automation and Systems, vol. 15, no. (3), pp. 976–985, June 2017.
T. Besselmann, J. Lofberg, and M. Morari, “Explicit MPC for LPV systems: Stability and optimality,” International Journal of Control, vol. 57, no. (9), pp. 2322–2332, September 2012.
X. Ping and B. Ding, “Off–line approach to dynamic output feedback robust model predictive control,” Systems & Control Letters, vol. 62, no. (11), pp. 1038–1048, November 2013.
D. Li and Y. Xi, “Design of robust model predictive Ccntrol based on multi–step control set,” Acta Automatica Sinica, vol. 35, no. (4), pp. 433–437, April 2009.
H. Li, D. Chen, H. Zhang, C. Wu, and X. Wang, “Hamiltonian analysis of a hydro–energy generation system in the transient of sudden load increasing,” Applied Energy, vol. 185, pp. 244–253, January 2017.
H. Li, D. Chen, H. Zhang, F. Wang, and D. Ba, “Nonlinear modeling and dynamic analysis of a hydro–turbine governing system in the process of sudden load increase transient,” Mechanical Systems and Signal Processing, vol. 80, pp. 414–428, December 2016.
Y. Su, K. K. Tan, and T. H. Lee, “Tube based quasi–minmax output feedback MPC for LPV systems,” IFAC Proceedings Volumes, vol. 45, no. (15), pp. 186–191, 2012.
X. Ping, “Output feedback robust MPC based on off–line observer for LPV systems via quadratic boundedness,” Asian Journal of control, vol. 19, no. (4), pp. 1641–1653, July 2017.
B. Ding, “Dynamic output feedback predictive control for nonlinear systems represented by a Takagi–Sugeno model, IEEE Transactions on Fuzzy Systems, vol. 19, no. (5), pp. 831–843, October 2011.
T. H. Kim and H. W. Lee, “Quasi–min–max outputfeedback model predictive control for LPV systems with input saturation,” International Journal of Control, Automation and Systems, vol. 15, no. (3), pp. 1069–1076, June 2017.
S. V. Raković, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, “Invariant approximations of the minimal robust positively invariant set,” IEEE Transactions on Automatic Control, vol. 50, no. (3), pp. 406–410, February 2005.
J. J. Martínez, “Minimal RPI sets computation for polytopic systems using the Bounded–real lemma and a new shrinking procedure,” IFAC–PapersOnLine, vol. 48, no. (26), pp. 182–187, 2015.
A. Alessandri, M. Baglietto, and G. Battistelli, “On estimation error bounds for receding–horizon filters using quadratic boundedness,” IEEE Transactions on Automatic Control, vol. 49, no. (8), pp. 1350–1355, August 2004.
A. Alessandri, M. Baglietto and G. Battistelli, “Design of state estimators for uncertain linear systems using quadratic boundedness,” Automatic, vol. 42, no. (3), pp. 497–502, March 2006.
G. Bitsoris, M. Vassilaki, and N. Athanasopoulos, “Robust positive invariance and ultimate boundedness of nonlinear systems,” Proc. of 20th Mediterranean Conference on Control & Automation, pp. 598–603, Barcelona, Spain, July 2012.
K. Derinkuyu and M. C. Pinar, “On the S–procedure and some variants,” Mathematical Methods of Operations Research, vol. 64, no. (1), pp. 55–77, August 2006.
P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI control toolbox for use with matlab, User’s guide, The Math Works Inc., Natick, MA, USA, 1995.
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Recommended by Associate Editor Andrea Cristofaro under the direction of Editor Myo Taeg Lim. This work was funded by the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6043), the National Nature Science Foundation of China (61773396, 61603285, 61403297).
Xu-Bin Ping received the Bachelor’s degree from Northwest University, Xi’an, China in 2005, the Master’s degree from the East China University of Science and Technology, Shanghai, China in 2008, and the Ph.D degree from Xi’an Jiaotong University, Xi’an, China, in 2013. His research interests include robust control, model predictive control.
Peng Wang was born in Shanxi Province of China. He received his Bachelor’s and Master’s degrees from Chang’an University, Shaanxi Province of China, in 2006 and 2009, respectively; and his Ph.D. degree from Xi’an Jiaotong University, Shaanxi Province of China in 2013. He is currently an associate professor with the Information and Navigation College, Air Force Engineering University. His research interests include receding horizon control, robust control, distributed estimation and distributed cooperative control.
Jia-Feng Zhang received the B.S. degree in automation from Xidian University, Xi’an, China in 2008, and the joint Ph.D by thesis “Modeling and verification of reconfigurable discrete event control systems” from Xidian University, Xi’an, China and Saarland University, Saarbrücken, Germany in 2015. She joined Xidian University, in 2015, where she is a lecturer of the School of Mechano-Electronic Engineering and a researcher of Systems Control and Automation Group.
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Ping, XB., Wang, P. & Zhang, JF. A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance. Int. J. Control Autom. Syst. 16, 2157–2168 (2018). https://doi.org/10.1007/s12555-017-0630-0
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DOI: https://doi.org/10.1007/s12555-017-0630-0