Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach

Abstract

Abstract This paper deals with designing a robust controller with H∞ performance index criteria for regulating the glucose-insulin level in type 1 diabetes. The proposed approach employs a Takagi-Sugeno (TS) fuzzy modeling and fuzzy model-based parallel distributed compensation (PDC) and non-parallel distributed compensation (non-PDC) schemes to design a stabilizing control law for the injecting insulin in silico. Deploying a non-quadratic Lyapunov function (NQLF) candidate, the stabilization conditions are derived in terms of linear matrix inequalities (LMIs) and solved by convex optimization techniques. Furthermore, based on the convex property of the membership functions, a new null term is defined which increases the degree of freedom of the proposed LMI constraints and reduces the stabilization conditions conservativeness. The diabetes models that are considered are nonlinear minimal Bergman and Tolic models that describe the glucose-insulin process in diabetes type 1. Based on the so-called sector nonlinearity approach (SNA), the equivalent TS fuzzy models of the Bergman and Tolic models are obtained. Then, the stabilization LMI conditions are solved and the PDC and non-PDC controllers are designed. Simulation results are obtained with a single patient testing parameters uncertainties and verify the advantages of the proposed robust control technique in dealing with the effects of external meal disturbance and maintaining the blood glucose concentration in the desired region to avoid the hypoglycemia and hyperglycemia disorders.