High Order Sliding Mode Controller for blood glucose in type 1 diabetes, with relative degree fluctuations

Glucose is regulated by insulin injections in patients with diabetes type 1. High Order Sliding Mode Controllers are well suited to perform a closed loop control due to is a non linear control, robust with respect to parameter uncertainties, and model unaccounted dynamics. These features represents an advance to other works in this field, due to the system is non linear, variable in the time, and the parameter identification is expensive and invasive to the patient. The improving of the model of glucose-insulin regulatory system, considering additional dynamics, increases, arbitrarily, the model order. The theorem that ensures the robustness of HOSMC with respect to unaccounted dynamics is given. This theorem justify the implementation of a controller designed for a reduced model will be able to handle the dynamics of a extended model. In this paper the theorem is illustrated by the design of a third order sliding mode controller, based on BeM, and tested also in SoM that is one of the most complete models and have 24 differential equations and has relative degree five.