Prescribed finite-time backstepping control for blood glucose regulation in type 1 diabetes

Automated blood glucose regulation in Type 1 diabetes (T1D) is challenging due to nonlinear glucose-insulin dynamics and meal-induced disturbances. Existing control strategies lack guaranteed finite-time convergence, risking prolonged hyperglycemia and hypoglycemia post-meals. We propose a novel prescribed finite-time backstepping controller derived from the Bergman Minimal Model (BMM), enforcing user-defined convergence bounds to ensure glucose stabilization within a pre-specified duration, regardless of meal variability. The control law guarantees finite-time convergence through Lyapunov stability. The efficiency and efficacy of the proposed approach are tested through case studies involving varying pre-specified time windows, meal variability, and physiological variability across patients. The proposed method outperforms existing conventional backstepping controllers and sliding mode control approaches, ensuring smooth, stable, and efficient regulation of blood glucose levels within defined time constraints while avoiding hypoglycemic events. The method's prescribed finite-time convergence ensures safety-critical performance, addressing a key limitation of prior approaches.