Robust Optimal Impulsive Blood Glucose Control Exploiting a Direct Searching Algorithm

In spite of numerous developments in blood glucose control based on the artificial pancreas, multiple daily injections (MDIs) are still the most applicable method in insulin-dependent diabetes mellitus (IDDM) subjects. These patients measure their blood glucose level (BGL) regularly and inject insulin in multiple dosages. In the present study, an efficient, robust optimal impulsive control approach is introduced to attain a safe range of blood glucose considering everyday life factors, including exercise, food intake, and circadian rhythms. This article assumes the dosages of the MDIs as control design parameters and addresses an appropriate approach for optimal dosage determination. The BGL regulation problem by the MDI program is characterized as a robust optimal impulsive control problem with uncertainties, and it is required to minimize the BGL error as the objective function. To achieve this, the polytopic form of the nonlinear glucose-insulin system is derived, and the feasible region for MDI is determined using a direct searching algorithm. Then, the optimal MDI is found by a sequential quadratic programming (SQP) approach. Regarding several uncertainties and the impulsive nature of insulin injection dosages, the proposed approach efficiently solves the BGL regulation problem. The proposed approach is evaluated by a simulated model of the blood-glucose insulin system in two regular and overfeeding scenarios with (mild, moderate) and without physical activity. The results show that the proposed method reduces the amount of injected insulin from 14% to 20% compared to a state-of-the-art approach and, simultaneously, reduces the severe hyperglycemia risk from 15% to 25% for overeating in three injection scenarios.