Identification of Time-Varying Manual-Control Adaptations with Recursive ARX Models

Time-varying human-operator (HO) adaptation in basic manual-control tasks is barely understood, as most HO identification methods do not explicitly take into account time variations. An identification procedure based on both batch and recursive autoregressive exogenous (ARX) models is used in this paper for captur- ing HO adaptation to time-varying changes in controlled-element dynamics in compensatory tracking tasks. Conditions with constant controlled-element dynamics, matching recent experimental work, and gradual and sudden transitions in the controlled-element dynamics were compared by means of Monte Carlo simulations with different remnant noise intensities. Overall, with batch ARX model identification results for conditions with constant dynamics, it is shown that differences between remnant noise and HO dynamics, both of which are directly coupled in the ARX model structure, will bias the identified ARX model parameters. Nevertheless, recursive ARX model identification results were still found to provide a reasonably estimate of time-varying HO model parameters for the tested time-varying scenarios. A direct comparison of using a constant scalar forgetting factor and a constant forgetting matrix, containing separate forgetting factors for each ARX model parameter, showed that a forgetting matrix did not result in a significant improvement for the considered HO identification problem. A forgetting factor of = 0.99609, corresponding to a memory horizon of 256 samples at 100 Hz, is found to be optimal for all tested conditions. An evaluation of real experimental manual-control data shows that, with straightforward online implementation, the method has potential as a tool for investigating, modeling, and measuring operators’ adaptive control characteristics.