Identification of Continuous-Time Hammerstein System with Nuclear Norm Convex Relaxation

• Published in: 东华大学学报（英文版） Vol. 32; no. 5; pp. 777 - 781
• Main Author: 戴明祥 何颖 杨新民 易文俊
• Format: Journal Article
• Language: English
• Published: Science and Technology on Transient Physics Laboratory, Nanjing University of Science and Technology, Nanjing 210094, China 31.10.2015
• Subjects: pseudospectral approximation; continuous-time (CT) Hammerstein system; nuclear norm convex relaxation
• ISSN: 1672-5220

The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time（ CT） Hammerstein system. The CT Hammerstein system is composed of a linear time invariant（ LTI） system and a static nonlinear function（ the linear part is followed by the nonlinear part）. The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output（ MISO） linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.