Frequency-domain subsystem identification with application to modeling human control behavior

Abstract

We present a frequency-domain subsystem identification algorithm that identifies unknown feedback and feedforward subsystems that are interconnected with a known subsystem. This method requires only accessible input and output measurements, applies to linear time-invariant subsystems, and uses a candidate-pool approach to ensure asymptotic stability of the identified closed-loop transfer function. We analyze the algorithm in the cases of noiseless and noisy data. The main analytic result of this paper shows that the coefficients of the identified feedback and feedforward transfer functions are arbitrarily close to the true coefficients if the data noise is sufficiently small and the candidate pool is sufficiently dense. This subsystem identification approach has application to modeling the control behavior of humans interacting with and receiving feedback from a dynamic system. We apply the algorithm to data from a human-in-the-loop experiment to model a human’s control behavior.