Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

Abstract

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.

Keywords:

• pure-feedback nonlinear stochastic systems
• adaptive fuzzy control
• dead-zone
• backstepping

Acknowledgements

This work is partially supported by the Natural Science Foundation of China (61074008, 61174033 and 11226139).

Additional information

Notes on contributors

Huanqing Wang

Huanqing Wang received the BSc degree in mathematics from Bohai University, Jinzhou, China, in 2003, and the MSc degree in mathematics from Inner Mongolia University, Huhhot, China, in 2006. Since 2006, he has been with School of Mathematics and Physics of Bohai University, Jinzhou, China. Now, he is a PhD candidate with the Institute of Complexity Science, Qingdao University, Qingdao, China. His research interest includes nonlinear control, adaptive neural control, and stochastic systems.

Bing Chen

Bing Chen received the BA degree in mathematics from Liaoning University, Shenyang, China, the MA degree in mathematics from the Harbin Institute of Technology, Harbin, China, and the PhD degree in electrical engineering from Northeastern University, Shenyang, in 1982, 1991, and 1998, respectively. He is currently a Professor with the Institute of Complexity Science, Qingdao University, Qingdao, China. His research interests include nonlinear control systems, robust control, and adaptive fuzzy control.

Chong Lin

Chong Lin received the BSc and MSc degrees in applied mathematics from Northeastern University, Shenyang, China, in 1989 and 1992, respectively, and the PhD degree in electrical and electronic engineering from Nanyang Technological University, Singapore, in 1999. In 1999, he was a Research Associate with the Department of Mechanical Engineering, University of Hong Kong, Hong Kong. From 2000 to 2006, he was a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. Since 2006, he has been a Professor with the Institute of Complexity Science, Qingdao University, Qingdao, China. He has authored or coauthored more than 60 research papers and coauthored two monographs. His current research interests include systems analysis and control, robust control, and fuzzy control.