Optimal Blood Glucose Control Through Continuous Insulin Infusion (2022)
In this paper, we formulate the problem of the insulin supply regimen in a diabetic patient as an optimal control problem, so that there is no overdose or insufficiency of the hormonal drug under different feeding styles. The interaction between glucose and insulin is modeled as a nonlinear system of ordinary differential equations. We prove the existence and global uniqueness of the solution of the system, as well as for the optimal control. The optimal control problem is solved directly by using the quadratic sequential programming method. The numerical results suggest setting, according to the patient’s dietary style, the prescribed glucose concentration level to be maintained during the day. The analytical and numerical study of this proposal is expected to be helpful in future insulin pump developments.