Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

Abstract

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.

Keywords:

• stochastic nonlinear systems
• output feedback
• neural network
• dynamic surface control
• variable separation

Acknowledgements

The authors would like to thank the editors and reviewers for their kind help and their valuable comments which greatly improved this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Natural Science Foundation of P.R. China [grant number 61304071], [grant number 71271132], [grant number 61403139]; the Natural Science Foundation of Shanghai [grant number 12ZR1408200]; the Science and Technology Commission of Shanghai Municipality [grant number 14YF1404500]; the Fundamental Research Funds for the Central Universities and the CSC scholarship.

Notes on contributors

Zhaoxu Yu

Zhaoxu Yu received his BS degree in mathematics from Jiangxi Normal University in 1998, MS degree in applied mathematics from Tongji University in 2001 and PhD degree in control science and engineering from Shanghai Jiaotong University in 2005. He is currently an associate professor with the Department of Automation in East China University of Science and Technology in Shanghai. His research interests include nonlinear control, adaptive control and stochastic system.

Shugang Li

Shugang Li is an associate professor in the School of Management at Shanghai University, Shanghai, China. He received his PhD degree in control engineering from Shanghai Jiao Tong University in 2004. His current research areas of interest are information system and information management, data mining, soft computing and artificial intelligence.

Fangfei Li

Fangfei Li received her BS degree from Liaoning Normal University in Dalian, in 2004, MS degree from University of Shanghai for Science and Technology in Shanghai, in 2007 and PhD degree from Tongji University in Shanghai, in 2012. Since 2012 she is serving as a lecturer at the Department of Mathematics, East China University of Science and Technology in Shanghai. Her research interests include Boolean networks, impulsive hybrid systems, systems biology etc.