Analysis of the islets-based glucose control system involving the nonlinear glucose-insulin metabolism model

Maintaining blood glucose concentration within a normal range is very important to diabetic patients. Many control algorithms, including the PID method, have been proposed to restore normal glucose tolerance via closed-loop insulin regulation. This paper analyzes the physiologically plausible glucose feedback control system involving the islets-based controller and the nonlinear pharmacokinetic model for glucose and insulin interactions. The model consists of six differential equations, and the islets-based controller is represented by a sigmoidal function. Our study reveals that, unlike most controllers, the islets-based controller's glucose setpoint cannot be explicitly set because it is implicitly determined by the parameters of the controller and model. We establish mathematical formulas relating the setpoint to the controller gain and to the steady states of other variables in the model. We also use the Lyapunov's linearization stability criterion to investigate system's local stability for a range of setpoint values. Finally, our simulation study shows that the islets-based controller moderately outperforms the linear PID controller optimized by a genetic algorithm. We conclude that developing more and better physiologically-inspired glucose controllers is important and promising. More research in that direction is needed.