Robust Polytopic-LPV Body-Weight-Dependent Control of Blood Glucose in Type-1 Diabetes

Abstract

This paper presents a robust $\boldsymbol {H}_{\infty }$ polytopic Linear Parameter Varying (LPV) controller to regulate the blood glucose level in type-1 diabetes patients. The suggested approach utilizes an observer-based controller and polytopic inexact gain-scheduling scheme to construct the stabilizing injecting insulin resilient against the external meal and snack disturbance in Silico. To assure the closed-loop stability and prescribed $\boldsymbol {H}_{\infty }$ performance, a Quadratic Lyapunov Function (QLF) is used and the stabilization conditions are derived in terms of Linear Matrix Inequalities (LMIs). The conventional minimal Bergman model is improved by considering the effect of body-weight on the glucose-insulin phenomenon and the new body-weight functions are identified based on real data. Then, for the body-weight-dependent Bergman model, a polytopic-LPV model is obtained. Simulations show the advantages of the developed glucose-insulin model and the robustness of the suggested controller in dealing with the effects of a meal for patients with different weights and avoiding hypoglycemia and hyperglycemia disorders.

Keywords

• Bergman model
• body-weight effect
• dynamic output controller
• glucose-insulin system
• linear parameter varying (LPV) model