Methods for the Identification of Time-Varying Hammerstein Systems with Applications to the Study of Dynamic Joint Stiffness

Abstract

The Hammerstein system provides a good model for the stretch reflex contribution to joint stiffness under quasi-stationary conditions. However, the model parameters change dramatically with the operating point defined by the joint angular position and muscle activation. Both position and activation level undergo large, rapid changes during movement and consequently reflex stiffness will be timevarying. Our laboratory has developed a series of algorithms to identify time-varying Hammerstein systems using approaches involving: large input-output ensembles, multiple short segments, temporal expansion, and linear parameter variation. This paper reviews these methods and evaluates their relative strengths and weaknesses.