Comparison of Regression Methods on Data-Driven Controller Design for Systems with Observation Noise

Abstract

Data-driven control design is one of the hot-topic in control. Among them, Fictitious Reference Iterative Tuning (FRIT) is considered useful, and some practical examples have been reported. However, few studies have considered the effect of observation noise and disturbance on FRIT, and there are no studies that have mathematically analyzed the influence of noise and disturbance on FRIT. In this paper, regression equation is derived from an optimization problem of FRIT and identical control parameters. As a result, residuals of the regression equation are colored, and optimized result of normal least squares method has bias. In response to this analysis, three regression methods which often employed in system identification are tested in a numerical example. All of the three methods are implemented as functions in MATLAB software, and it is easy to actually use.