Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator

Abstract

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique.

Keywords:

• anti-windup
• discrete-time Markovian jump systems
• norm-bounded uncertainties
• partly known transition probabilities
• saturating actuators
• linear matrix inequality (LMI)

Acknowledgements

This work was partially supported by a research grant from the Australian Research Council; National Natural Science Foundations of PR China under Grants 61273123, 61203056; the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20113219110026; NSFC 61203048.

Additional information

Notes on contributors

Yunliang Wei

Yunliang Wei was born in Jining, Shandong Province, P. R. China, in 1984. He received his BS degree in Mathematics and Applied Mathematics from Qufu Normal University, Qufu, Shandong Province, P. R. China, in 2008. He is now a PhD candidate in Control Science and Engineering at the School of Automation, Nanjing University of Science and Technology, Nanjing, P. R. China. Since January 2013, he has been with the School of Computing, Engineering and mathematics at the University of Western Sydney as a visiting student. His current research interests include hybrid systems, nonlinear systems, robust control, actuator saturation and anti-windup design.

Wei Xing Zheng

Wei Xing Zheng received the PhD degree in Electrical Engineering from Southeast University, China in 1989. He has held various faculty/research/visiting positions at Southeast University, China, Imperial College of Science, Technology and Medicine, UK, University of Western Australia, Curtin University of Technology, Australia, Munich University of Technology, Germany, University of Virginia, USA and University of California-Davis, USA. Currently, he holds the rank of Full Professor at University of Western Sydney, Australia. Dr Zheng has served as an Associate Editor for several flagship journals including IEEE Transactions on Automatic Control and Automatica.

Ze Li

Ze Li received the B.Sc. degree from Nanjing University of Science and Technology, Nanjing, China, in 2005 and the PhD degree from Nanjing University of Science and Technology, Nanjing, China, in 2010 (combined M-PHD programme). Since February 2010, she has joined the College of Electronic & Information Engineering, Suzhou University of Science and Technology, where she is currently a Lecturer. Her research interests include robust control and filtering, time-delay systems, stochastic systems, nonlinear systems and fuzzy systems.

Guangdeng Zong

Guangdeng Zong received his PhD degree in control theory and application from Southeast University, Nanjing, P. R. China in 2005. His major research interests include: BAM neural networks, switched systems and time-delay systems theory. From February 2010 to August 2010, and June 2012 to June 2013, he was a visiting scholar in the Department of Electrical and Computer Engineering, Utah State University, and the School of Computing, Engineering and mathematics at the University of Western Sydney, respectively. Currently, he is a professor in Research Institute of Automation at Qufu Normal University.