Optimization formalization of diabetes treatment procedure

A formalization of the problem associated with diabetes therapy based on successive injections of insulin in order to minimize the quadratic deviation of the current glucose concentration from the normal level is given. Modeling of this procedure is carried out in a continuous-discrete version in the terminology of optimal control. The phase system is described by differential equations, permissible controls, phase constraints and the target functional are formalized in discrete time on a given grid of values. As a result, a special quadratic programming problem is constructed, which allows an effective solution in a finite number of iterations.