New identification method for Hammerstein models based on approximate least absolute deviation

Abstract

Disorder and peak noises or large disturbances can deteriorate the identification effects of Hammerstein non-linear models when using the least-square (LS) method. The least absolute deviation technique can be used to resolve this problem; however, its absolute value cannot meet the need of differentiability required by most algorithms. To improve robustness and resolve the non-differentiable problem, an approximate least absolute deviation (ALAD) objective function is established by introducing a deterministic function that exhibits the characteristics of absolute value under certain situations. A new identification method for Hammerstein models based on ALAD is thus developed in this paper. The basic idea of this method is to apply the stochastic approximation theory in the process of deriving the recursive equations. After identifying the parameter matrix of the Hammerstein model via the new algorithm, the product terms in the matrix are separated by calculating the average values. Finally, algorithm convergence is proven by applying the ordinary differential equation method. The proposed algorithm has a better robustness as compared to other LS methods, particularly when abnormal points exist in the measured data. Furthermore, the proposed algorithm is easier to apply and converges faster. The simulation results demonstrate the efficacy of the proposed algorithm.

Keywords:

• Hammerstein non-linear models
• approximate least absolute deviation
• stochastic approximation
• disorder and peak noises
• robustness

Additional information

Funding

This work was supported by China Scholarship Council [grant number 201206445008] and Science Foundation of China University of Petroleum, Beijing [grant number 01JB0161].

Notes on contributors

Bao-Chang Xu

Bao-Chang Xu was born in Heilongjiang, China, in 1974. He is currently an associate professor of control theory and control engineering in China University of Petroleum, Beijing, China. He received his Bachelor of Engineering degree in 1997 and his MS degree in 2000 from Northeast Petroleum University, and his PhD degree from Beijing University of Aeronautics and Astronautics, China, in 2005. His research interests include system identification and advanced control, image processing, multi-sensor data fusion and soft sensor technology.

Ying-Dan Zhang

Ying-Dan Zhang was born in Liaoning, China, in 1989. She received her MS degree in control science and engineering from China University of Petroleum (Beijing) in 2014 and joined the Urban Construction Design & Development Group Co. in Beijing in 2014. Her research interest is dynamic system identification