An Approximate Solution for Glucose Model via Parameterization Method in Optimal Control Problems

Glucose tolerance test is advised to detection of pre-diabetics and mild diabetics in the medical practice. Several mathematical models such as glucose model, were proposed for mimicking the blood glucose-insulin interaction. To predict accurate insulin requirement for each glucose concentration, we need to solve optimal control problems. In this model, constraints are linear and nonlinear forms of cost function. Although ordinary methods can be used in glucose model, but non-negative natures of medical variables made them difficult to use. To finding a new approximate solution of glucose model, parameterization method with non-negative coefficients in polynomial was used. In this state parameterization method, we use polynomials that ensure that the control variable is non-negative in this model. And increases the time for the model solution to be non-negative compared to conventional methods. The simplicity, lower requirement for mathematical calculations and more compatibility with variables are positive aspects of our parameterization method.