Algorithms for a closed-loop artificial pancreas: the case for model predictive control

Abstract

The relative merits of model predictive control (MPC) and proportional-integral-derivative (PID) control are discussed, with the end goal of a closed-loop artificial pancreas (AP). It is stressed that neither MPC nor PID are single algorithms, but rather are approaches or strategies that may be implemented very differently by different engineers. The primary advantages to MPC are that (i) constraints on the insulin delivery rate (and/or insulin on board) can be explicitly included in the control calculation; (ii) it is a general framework that makes it relatively easy to include the effect of meals, exercise, and other events that are a function of the time of day; and (iii) it is flexible enough to include many different objectives, from set-point tracking (target) to zone (control to range). In the end, however, it is recognized that the control algorithm, while important, represents only a portion of the effort required to develop a closed-loop AP. Thus, any number of algorithms/approaches can be successful--the engineers involved in the design must have experience with the particular technique, including the important experience of implementing the algorithm in human studies and not simply through simulation studies.

Figure 1.

Basic concept of MPC. At the current time step, a model is used to predict the effect of proposed current and future manipulated input (insulin infusion) changes on the desired output (glucose) over a prediction horizon. Minimum and maximum (constraints) infusion rates can be enforced. Notice that the prediction horizon is often larger than the control horizon. P, prediction horizon; M, control horizon.

Figure 2.

Performance of controllers averaged over the nine valid simulated subjects. Enhanced MPC is the MMPPC strategy. The PID controller parameters were adjusted to minimize the blood glucose risk index averaged over the subjects. The MPC represents a “standard” MPC strategy with a symmetric objective function. The basal–bolus strategy represents optimal performance and is based on perfect meal knowledge; none of the other strategies used meal anticipation. Figure reproduced with permission from Cameron and coauthors. CHO, carbohydrate; BG, blood glucose; EMPC, enhanced model predictive control; BB, basal–bolus.