Page 291 - Glucose Monitoring Devices

298 CHAPTER 15 Automated closed-loop insulin delivery

the glucose-insulin system that is used to predict in open loop the future evolution
trajectory of the glycemic dynamics; (ii) a performance index such as the quadratic
difference between predicted and target glucose values to be minimized over a finite
time horizon subject to constraints imposed by the glucose-insulin model, restric-
tions on the maximum allowable insulin infusion (control inputs), and system states
to obtain a trajectory of optimal future insulin infusions at each sampling time; and
(iii) a receding-horizon implementation scheme that introduces feedback in the
control law with new glucose measurements and updated state information at
each sampling instance to compensate for disturbances (meals and physical activity)
and modeling errors. The reliance on a glucose-insulin model means that the effec-
tiveness of the controller depends highly on the accuracy of the model. Fig. 15.1
illustrates the mechanism of MPC.
Consider a discrete-time glucose-insulin dynamic system as

x kþ1 ¼ fðx k ; u k Þ
y k ¼ gðx k ; u k Þ
where x denotes the state of the system, y denotes the output glucose measurements,
and u denotes the inputs (infused insulin) and with constraints on the insulin infusion
generalized as hðx k ; u k Þ 0. The MPC formulation that regulates the glucose con-
centrations involves solving, for each current system state x, the following con-
strained optimal control problem

V N ðxÞ¼ min Jðx; uÞ
x 0 ;u 0 ;.;x N

FIGURE 15.1
A diagram of the MPC algorithm with the model used to predict the future sequence of
glucose measurements and an optimization approach used to select the best input
sequence that minimizes the deviation of the predicted outputs from the reference
set-point trajectory.