Page 293 - Glucose Monitoring Devices

300 CHAPTER 15 Automated closed-loop insulin delivery

in a predefined zone, such as a desirable euglycemic zone. An inherent benefit of
control to the zone is that the pump actuation and infusion activity will be inherently
limited when the glucose levels are within the defined zone. The lack of corrective
suggestions when glycemic measurements are within the desired zone has the poten-
tial to reduce power consumption on handheld and mobile devices typically running
the control algorithms [14,29].
The novelty of the zone MPC algorithm lies in the cost function formulation.
Zone MPC, analogous to typical MPC algorithms, predicts the dynamic future tra-
jectory profile of the glycemic values using an explicit model of the glucose-insulin
dynamics and a candidate input trajectory to be optimized. In contrast to typical
MPC that drives the controlled variable to a specific fixed set-point, the optimization
problem in zone MPC attempts to maintain or drive the predicted outputs into a pre-
defined zone described by upper and lower bounds [29,58]. The optimization prob-
lem of zone MPC for a given current state x is

V N ðxÞ¼ min Jðx; uÞ
x 0 ;u 0 ;.;x N
subject to:

x 0 ¼ x
x kþ1 ¼ fðx k ; u k Þ; k˛I 0:N 1
k˛I 0:N
y k ¼ gðx k ; u k Þ
hðx k ; u k Þ 0; k˛I 0:N
x k ˛X; u k ˛U; k˛I 0:N
where the objective function JðxÞ is defined by
N
X range T range s T s
y Q k y
k k
Jðx; uÞ¼ þðu k u Þ R k ðu k u Þ
k¼0
with y range as the superposition of all the predicted glucose outputs exceeding the
permitted euglycemic range, and is given by
h i
range lo lb hi ub
y ¼ y y ; y y
k k k
Further, y lo and y hi denote the aggregation of all predicted controlled outputs
k k
lb
ub
lb
below the lower bound y and above the upper bound y , where y and y ub char-
acterize the desired glycemic range. This aggregation is conducted by setting all pre-
lb ub
dicted output values that are within the safe target range ½y y Š to zero as follows:
lb
lo y k if y k < y
k
y ¼
0 otherwise
and
ub
hi y k if y k > y
k
y ¼
0 otherwise