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

ABSTRACT

This paper focuses on an adaptive fuzzy tracking control problem for a class of pure-feedback stochastic nonlinear systems with unknown dead zone outputs. To overcome the design difficulty arising from the nonlinearity in the output mechanism, the new properties of Nussbaum function are employed and an auxiliary virtual controller is constructed. The proposed adaptive fuzzy control method guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighbourhood of the origin in the sense of mean quartic value. Simulation results further demonstrate the effectiveness of the presented control algorithm.

KEYWORDS:

• Pure-feedback stochastic nonlinear systems
• unknown dead zone outputs
• Nussbaum function
• adaptive fuzzy control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61573227, 61633014, 61703248], the Research Fund for the Taishan Scholar Project of Shandong Province of China, and SDUST Research Fund [grant number 2015TDJH105].

Notes on contributors

Hang Su

Hang Su received her M.S. degree from Shandong University of Science and Technology, Qingdao, China, in 2014. She is currently a Ph.D. candidate of Shandong University of Science and Technology, Qingdao, China. Her main research interests include fuzzy control, adaptive control and stochastic nonlinear control systems.

Weihai Zhang

Weihai Zhang (SM'16) received his M.S. degree from Hangzhou University (currently, Zhejiang University), and the Ph.D. degree from Zhejiang University, Hangzhou, China, in 1994 and 1998, respectively. He is currently a Professor of Shandong University of Science and Technology. Dr Zhang is a Taishan Scholar of Shandong Province of China, and serves as an Associate Editor for Asian Journal of Control, International Journal of Fuzzy Systems and Journal of the Franklin Institute. Dr Zhang is a Senior Member of IEEE and a Member of Technical Committee on Control Theory of Chinese Association of Automation. Dr Zhang has published more than 120 peer reviewed journal papers and one monograph (Zhang, W., Xie, L., & Chen, B. S., Stochastic H₂/H_∞ control: A Nash game approach, Boca Raton, FL: CRC Press, 2017). Dr Zhang has won the second prize of the Ministry of Education of the People's Republic of China twice. His research interests include linear and nonlinear stochastic optimal control, mean-field systems, robust H_∞ control, stochastic stability and stabilisation, multi-objective optimisation, and fuzzy adaptive control.