  Data-driven controls using Gaussian process regression have recently gained
much attention. In such approaches, system identification by Gaussian process
regression is mostly followed by model-based controller designs. However, the
outcomes of Gaussian process regression are often too complicated to apply
conventional control designs, which makes the numerical design such as model
predictive control employed in many cases. To overcome the restriction, our
idea is to perform Gaussian process regression to the inverse of the plant with
the same input/output data for the conventional regression. With the inverse,
one can design a model reference controller without resorting to numerical
control methods. This paper considers single-input single-output (SISO)
discrete-time nonlinear systems of minimum phase with relative degree one. It
is highlighted that the model reference Gaussian process regression controller
is designed directly from pre-collected input/output data without system
identification.
