A backstepping control of artificial pancreas for type 1 diabetes based on sub-fixed-time stability

The artificial pancreas device is an automated control system that simulates the function of the human pancreas. It continuously infuses insulin into the body, thereby maintaining the blood glucose levels of diabetic patients within a safe range. This device is expected to be widely adopted for patients with type 1 diabetes in the future. Currently, research on artificial pancreas control methods is still in its early stages. Most existing blood glucose control methods rely on controller designs that incorporate only gain parameters and typically lack rigorous theoretical analysis of closed-loop system stability. In contrast, the Power Exponent Controller (PEC), which introduces power exponent parameters, belongs to the categories of finite-time or fixed-time control. These controllers often demonstrate superior overall performance in terms of convergence rate, robustness, and other critical control metrics.

This paper proposes an insulin infusion rate based on PEC. A comprehensive stability analysis of the blood glucose closed-loop system is conducted using backstepping control theory, particularly providing mathematical expressions for system convergence time and steady-state error. The proposed control method is evaluated through three sets of simulation experiments comparing it with a traditional homogeneous control method.

The theoretical findings suggest that the proposed control method effectively reduces disturbances caused by meals and the infusion process, allowing quick adjustment of the patient's blood glucose to the target range. The results from the three sets of simulation experiments demonstrate that, compared to the traditional homogeneous control method, the proposed PEC scheme offers several advantages: a faster and more responsive reduction in hyperglycemia; the ability to consistently maintain postprandial glucose peaks below 180 mg/dL despite glucose fluctuations caused by three daily meals; and a reduction of approximately 25 minutes in the time required to bring blood glucose into the safe range during extreme daily regulation scenarios involving initial hyperglycemia.

These findings indicate that the proposed PEC method provides improved performance for artificial pancreas systems, with potential benefits for clinical management of type 1 diabetes.