In diabetes mellitus, the efficient alleviation of hyperglycemia, an elevated glycemic concentration, is quite crucial to avoid persistent complications. Thus, it is of prime importance to have an automated closed-loop insulin delivery system, often termed as an artificial pancreas, in the patient's body. The requisite amount of exogenous insulin bolus must be determined by a control algorithm, which is the primary constituent of the closed-loop system. In this article, a finite-time synergistic control approach, based on a gain-scheduled Luenberger observer (GSLO), is introduced. The proposed control strategy establishes a closed-loop insulin delivery system, which confirms the glycemic regulation that is quite obligatory in type-1 diabetic (T1D) patients. The control law is synthesized by using a recursive backstepping with a sliding mode control (SMC) approach. Besides, the nonlinear terms are incorporated, in the pseudo control inputs, which provide the finite-time convergence of the system's trajectories. Since the proposed control law relies on the system's information, thus, a virtual patient simulator, presented by Bergman minimal model (BMM), is transformed into an equivalent dynamic structure, which facilitates the design of GSLO. The observer's gains, which modify in each iteration, are based on the updated values of the system's states. Also, it endorses the separation principle, thus proving the closed-loop system's stability. The proposed closed-loop insulin delivery system confirms the suppression of postprandial hyperglycemia and hypoglycemic events in T1D patients. The efficacy is demonstrated via in-silico testing, which is executed in MATLAB/Simulink environment. INDEX TERMS Gain-scheduled Luenberger observer, glucose-insulin stabilization, recursive backstepping method, sliding mode control approach, closed-loop insulin delivery system, Bergman minimal model, external disturbances, controllable canonical system.
