we then train both our proposed method and an algorithm as in [@Luo.2016; @Kiumarsi.2014] which assumes that the reference always follows the dynamics of an exo-system ${\boldsymbol{f}}_{\text{ref}}({\boldsymbol{r}}_k)$ (in the following termed *comparison algorithm*). The comparison algorithm is trained on the augmented system $$\begin{aligned}
\label{eq:augmented_sys}
{\boldsymbol{x}}_{\text{aug},k+1}={\begin{bmatrix*}[c]{\boldsymbol{A}}&{\boldsymbol{0}}\\{\boldsymbol{0}}&{\boldsymbol{F}}_{\text{ref}}
\end{bmatrix*}}{\boldsymbol{x}}_{\text{aug},k}+{\begin{bmatrix*}[c]{\boldsymbol{B}}\\ {\boldsymbol{0}}
\end{bmatrix*}}{\boldsymbol{u}}_k,\end{aligned}$$ where ${\boldsymbol{x}}_{\text{aug},k}={\begin{bmatrix*}[r]{\boldsymbol{x}}_k^\intercal&{\boldsymbol{r}}_k^\intercal
\end{bmatrix*}}^\intercal$. After the training, we vary $\alpha_{\text{ref}} = y_{\text{ref}}$ (arbitrary references such as different frequencies, ramps and steps) in order to show that the controller learned with our method successfully generalizes to these references. In contrast, we show the resulting behavior of the comparison algorithm which is constructed on the assumption that the reference dynamics always follows .

Our evaluation is twofold. On one hand, after the learning process has finished, we analyze the root mean square (RMS) tracking errors $\alpha_{\text{RMS}}$ and $y_{\text{RMS}}$ between the learned tracking behavior by means of the trajectory $\alpha_{\text{learned}}$ and $y_{\text{learned}}$ where the system dynamics is unknown (both for our algorithm and the comparison algorithm) and the optimal solution $\alpha_{\text{opt}}$ and $y_{\text{opt}}$ which results from Theorem \[Theo:Q\] and known system dynamics. On the other hand, we compare the learned weights ${\boldsymbol{w}}$ of our algorithm with the optimal solution ${\boldsymbol{w}}^*$ (weights corresponding to Theorem \[Theo:Q\] and 