Methods of computational optimization for automated insulin therapy control

The control automation of insulin-dosing technical systems for patients with type 1 diabetes mellitus is an urgent task of biomedical engineering. The development of computing technologies allows using complex nonlinear predictive models for calculating optimal control actions. The use of such models makes it necessary to develop efficient methods for numerically solving stiff systems of nonlinear ordinary differential equations, developing efficient methods for parametric identification of mathematical models and developing efficient methods for optimizing control actions. The paper presents a set of studies and numerical experiments aimed at formalizing computational problems, identifying known methods and algorithms for solving the problems and experimentally evaluating the efficiency of selected methods and algorithms. It is demonstrated that the LSODA algorithm is efficient in numerically solving the model equations, using the Adams method when in nonstiff areas and the backward differentiation formula on stiff areas. A method for optimizing parametric identification is proposed by using the «basin hopping» global optimization method with a Nelder–Mead local minimizer. For solving the problem of multidimensional conditional optimization of control actions, the COBYLA method has shown the highest efficiency, ensuring the finding of optimal parameters on household computers in an acceptable time.