Abstract
A convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach.
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Recommended by Associate Editor Niket Kaisare under the direction of Editor Jay H. Lee. This work was funded by the National Nature Science Foundation of China (61403297, 61973243), the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6043).
Xubin Ping received his Bachelor’s degree from Northwest University, Xi’an, China, in 2005 and his Master’s degree from the East China University of Science and Technology, Shanghai, China, in 2008 and a Ph.D. degree from Xi’an Jiaotong University, Xi’an, China, in 2013. His research interests include robust control, model predictive control.
Sen Yang received his Bachelor’s degree from Xi’an University of Science and Technology, Xi’an, China, in 2018. He is currently a Master student major in control science and engineering with Xidian University, Xi’an, China. His research interests cover model predictive control and its applications.
Baocang Ding was born in Hebei Province, China. He received his M.S. degree from the China University of Petroleum, Beijing, China, in 2000 and a Ph.D. degree from Shanghai Jiaotong University, Shanghai, China, in 2003. From September 2005 to September 2006, he was a Postdoctoral Research Fellow in Department of Chemical and Materials Engineering, University of Alberta, Canada. From November 2006 to August 2007, he was a Research Fellow in the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. From September 2003 to August 2007, he was an Associate Professor in Hebei University of Technology, Tianjin, China. From September 2007 to December 2008, he was a Professor in Chongqing University, Chongqing, China. From January 2009 to September 2019, he was a Professor in Xi’an Jiaotong University, Xi’an, China. He is currently a Professor with Chongqing University of Posts and Telecommunications, Chongqing, China. His research interests include predictive control, fuzzy control, networked control, and distributed control systems.
Tarek Raïssi received his Engineering degree from National Engineering School of Tunis in 2000, an Master degree in Automatic Control from Central School of Lille in 2001, a Ph.D. from the University of Paris XII in 2004 and the Accreditation to Supervise/Conduct Research (HDR) from the University of Bordeaux in 2012. From 2005 to 2011, he was an Associate Professor at the University of Bordeaux. Currently, He is a Full Professor at the Conservatoire National des Arts et Metiers, Paris, France. He is a member of the IFAC Technical Committee “Modeling, Identification and Signal Processing” and a Senior member of IEEE. His research interests include fault detection and isolation, nonlinear systems estimation and robust control.
Zhiwu Li received his B.S., M.S., and Ph.D. degrees in mechanical engineering, automatic control, and manufacturing engineering, respectively, all from Xidian University, Xi’an, China, in 1989, 1992, and 1995, respectively. He joined Xidian University in 1992 and now he is also with the Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau. Over the past decade, he was a Visiting Professor at the University of Toronto, Technion-Israel Institute of Technology, Martin-Luther University of Halle-Wittenburg, Conservatoire National des Arts et Métiers (CNAM), Meliksah Universitesi. His current research interests include Petri net theory and application, supervisory control of discrete event systems, workflow modeling and analysis, system reconfiguration, game theory, and data and process mining. He is a member of Discrete Event Systems Technical Committee of the IEEE Systems, Man, and Cybernetics Society, and a member of IFAC Technical Committee on Discrete Event and Hybrid Systems from 2011 to 2014. He serves as a frequent reviewer for 40+ international journals including Automatica and a number of the IEEE Transactions as well as many international conferences. He is listed in Marquis Who’s Who in the world, 27th Edition, 2010. Dr. Li is a recipient of an Alexander von Humboldt Research Grant, Alexander von Humboldt Foundation, Germany. He is a senior member of IEEE and is the founding chair of Xi’an Chapter of IEEE Systems, Man, and Cybernetics Society.
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Ping, X., Yang, S., Ding, B. et al. A Convexity Approach to Dynamic Output Feedback Robust MPC for LPV Systems with Bounded Disturbances. Int. J. Control Autom. Syst. 18, 1378–1391 (2020). https://doi.org/10.1007/s12555-019-0089-2
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DOI: https://doi.org/10.1007/s12555-019-0089-2