Synthesizing Robust Observer-Based Guaranteed Cost Linear Parameter Variable Control for Artificial Pancreas Systems Under Input Saturation

The artificial pancreas (AP), commonly known as a closed-loop insulin delivery control system, consists of three primary components: a glucose sensor for measuring blood glucose concentration (BGC), a control algorithm responsible for determining the rate of exogenous insulin delivery (IDR), and an insulin infusion pump. In this paper, a novel approach is introduced for designing a guaranteed cost observer-based linear parameter variable (GC-LPV) control system for blood glucose levels in Diabetic Patients. The Bergman Minimal Model (BMM), which is widely used for understanding the glucose-insulin regulatory system, is described as a Quasi-Linear Parameter Varying (QLPV) system. The main innovation of the paper lies in presenting a new method that optimizes performance without considering input in the cost function and the concurrent design of LPV observer and LPV controller. One notable aspect of the design conditions is the incorporation of input saturation considerations during the design process. This inclusion leads to performance improvement by addressing the constraint of insulin injection effectively. Another significant contribution of the paper is its unified approach to transforming the problem into a convex optimization problem, incorporating Linear Matrix Inequalities (LMIs). The proposed adaptive dynamic output structure provides flexibility in controller design while ensuring stability and performance, even in the presence of parametric uncertainty. Simulation results confirm that the GC-LPV controller yields improved performance compared to state-of-the-art methods.