Fig. 7:

Illustration of control penalty adaptation. In the upper panel, the red curve shows the trend of first element ${\text{y}}_1^i$ in the glucose prediction sequence ${\text{y}}_{1:N_p}^i$ with respect to discrete time i, while the green curves denote the sequences of ${\text{y}}_{1:N_p}^i$. Note that the red and green curves denotes glucose predictions, which are different from actual CGM measurements. In the lower panel, the dark blue curve shows the trend of $\hat{R}\left({\mu }_1^i,{\text{y}}_1^i\right)$ with respect to discrete time i, the light blue curves denote the sequences of $\hat{R}\left({\mu }_{1:N_p}^i,{\text{y}}_{1:N_p}^i\right)$, and the black line indicates the constant $\hat{R}$ adopted in [7]. The superscript i used here indicates the dependence of a variable on time.