Abstract:
A mathematical model is proposed to study the plasma glucose control for insulin therapy in a limited time. The objective function based on the integrated control effect of glucose is given according to the clinical treatment situation, and two different optimal injection strategies are investigated. To solve the technical problem in optimal impulsive control, a time rescaling method is applied and the gradient formulas of the objective function with respect to two control parameters (injection doses and injection timings) are obtained. In addition, using numerical simulations, the optimal injection doses and injection timings for each injection strategy are given. The results show that the optimal injection timing control is superior to the optimal injection dose control.