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Adaptive control of artificial pancreas systems for treatment of type 1 diabetes 71

the normalized PIC bounds with the basal PIC value. Therefore, appropri-
ate PIC bounds can be determined based on each subject’s basal PIC value
and the CGM measurement.

3.3 Feature extraction for manipulating constraints

Meal consumption can be automatically detected using qualitative descrip-
tions of glucose time-series data, which is useful in modifying the aggressive-
ness of the AL-MPC (Samadi et al., 2017, 2018). In this work, features are
generated from the data to describe the recent trajectory of the glycemic

measurements. To this end, a p-order polynomial y i ¼ ft i ,θ M with
k
parameters θ M is fitted to the most recent l glucose measurements
k
y i:i l :¼ y i y i 1 … y i l Š at each sampling time using ordinary least squares
½
where t i denotes the sampling index of the recent measurements. Then
the derivatives of the polynomial are obtained and the first- and second-
order derivatives, denoted f (1) and f (2) , are analyzed to derive parameter
P meal for detecting carbohydrate consumption as
8
f ð1Þ
> m
> if f ð1Þ c and f ð2Þ 0
>
c
> m 0
>
> 1
>
<
P meal ¼ f ð1Þ m (3)
if f ð1Þ c and f ð2Þ < 0
> 0
c
> m
>
> 2
>
>
>
0 if f < c
: ð1Þ m
0
m
m
m
where c , c , and c are patient-specific threshold parameters. Detection of
1 2 0
meals based on the P meal parameter allows for the constraints of the
AL-MPC are modified when meals are to make the controller more aggres-
sive to suggest a sufficient insulin dose.
3.4 Adaptive-learning MPC formulation
Here, we propose a novel AL-MPC algorithm cognizant of the PIC for
computing the optimal insulin infusion rate. In Fig. 2, different components
of the AL-MPC are shown as the order of computations to obtain the opti-
mum insulin doses. The proposed AL-MPC formulation employs the gly-
cemic and PIC risk indexes that manipulate the penalty weighting matrices
in the cost function. To this end, the AL-MPC computes the optimal insulin
infusion over a finite horizon using the identified time-varying subspace-
based models by solving at each kth sampling instance the following
quadratic programming problem