Simultaneous Parameter Estimation in Model-Free Control

Model-Free control is a data-driven control methodology that utilizes a surrogate model, namely the ultra-local mode, to provide a short-time estimate of the dynamics and uncertainties related to a nonlinear system. Traditional Model-Free control requires two parameters, one is estimated online while the other is considered a tuning parameter for the performance of the system at hand. The tuning parameter is typically chosen heuristically and depends upon expert knowledge of the system. This paper provides a methodology for on-the-fly simultaneous selection of all parameters of the ultra-local model. The procedure relies on a robust Kalman Filter and an optimization routine that enforces the validity of the ultra-local model. An illustrative example is provided where the methodology developed is shown to improve the tracking performance of a system and, more importantly, that the estimated parameters converge to the expected values of the system.