Glucose–insulin stabilization in type-1 diabetic patient: A uniform exact differentiator–based robust integral sliding mode control approach

Abstract

Diabetes mellitus is a persistent metabolic syndrome caused by impaired capability of the body’s production and usage of insulin. This impaired capability results in chronic hyperglycaemia, the elevated glucose concentration in the bloodstream, which may lead to many incurable complications. To escape this dire situation, a proper model-based exogenous infusion of insulin bolus is required, which is usually established via different feedback control strategies. In this article, the authors present a mathematical model–based robust integral sliding mode control approach for stabilization of internal glucose–insulin regulatory system in type-1 diabetic patient. Since the state variables of the system are not directly available to the controller, a uniform exact differentiator observer is employed to accomplish the aforementioned task. In the proposed control law, the incorporation of integral term in the switching manifold eliminates the reaching phase, which causes the sliding mode to establish from the very initial point, thus enhances the robustness property of the proposed control scheme. Moreover, the chattering problem is also substantially suppressed to a considerable extent along a defined manifold. To verify the theoretical analysis, the proposed control law is verified via computer simulations which demonstrate the effectiveness of the proposed control law against the external perturbations, that is, unannounced meal intake and physical exercise.