Adaptive control of Hammerstein–Wiener nonlinear systems

Abstract

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

Keywords:

• Hammerstein–Wiener nonlinear system
• adaptive control
• convergence properties
• closed-loop system stability
• adaptive weighted factor

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments to improve the quality of this note.

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China [grant numbers 61333006, 61473072].

Notes on contributors

Bi Zhang

Bi Zhang was born in Shenyang, Liaoning, China. He is currently studying for a PhD degree in the Northeastern University, Shenyang, China. His main research interests are nonlinear adaptive control and parameter estimation.

Hyokchan Hong

Hyokchan Hong is working towards his PhD degree at Northeastern University, China. His main research interests are nonlinear system modeling and control.

Zhizhong Mao

Zhi-Zhong Mao received his BS degree from Harbin Electrician College, Harbin, China in 1982, and the MS and PhD degrees from Northeastern University, Shenyang, China in 1984 and 1991 respectively. He is a professor and a PhD supervisor at Northeastern University, China. His main research interests are modeling, control and optimization in complex industrial systems.