A Non-Parametric Approach for Identification of Parameter Varying Hammerstein Systems

Abstract

This paper presents a novel method for non-parametric identification of parameter-varying (PV) Hammerstein systems where the parameters of both the static nonlinearity and the linear dynamics change with a scheduling variable. The proposed method estimates the individual elements of the PV Hammerstein system by describing the static nonlinear element using a PV Chebychev basis expansion and the linear dynamic element as a non-parametric PV impulse response function with Laguerre basis expansion. The method was validated using Monte-Carlo simulations of a PV Hammerstein model of ankle reflex stiffness during large movements. Results demonstrated that the method is simple, effective, and robust; it accurately identified the PV Hammerstein system in the presence of relatively large colored, time-varying measurement noise (average SNR of 15dB). These results demonstrate the two main contributions of the method: (1) It accurately and precisely estimates both the linear and nonlinear elements of the PV Hammerstein cascade as they vary with a scheduling variable; and (2) Models identified with the method accurately predict the response of the PV Hammerstein system to novel scheduling variable trajectories. To our knowledge, no other Hammerstein method can achieve these.

Keywords

• Biomedical systems
• Hammerstein systems
• identification algorithms
• joint stiffness
• parameter-varying models