Blood-glucose regulator design for diabetics based on LQIR-driven Sliding-Mode-Controller with self-adaptive reaching law

Type I Diabetes is an endocrine disorder that prevents the pancreas from regulating the blood glucose (BG) levels in a patient's body. The ubiquitous Linear-Quadratic-Integral-Regulator (LQIR) is an optimal glycemic regulation strategy; however, it is not resilient enough to withstand measurement noise and meal disruptions. The Sliding-Mode-Controller (SMC) yields robust BG regulation effort at the expense of a discontinuous insulin infusion rate that perturbs the BG concentrations. Hence, the novel contribution of this article is the formulation of a hybridized LQIR-driven SMC strategy that retrieves the benefits of the aforesaid control schemes while avoiding their inherent problems. The proposed control approach is realized by linearly combining a glycemic LQIR law with an innovative sign function sliding mode reaching law that is driven by a customized LQIR-driven sliding surface. The hybridized control scheme generates optimal control decisions yielded by the LQIR while mimicking the robustness characteristic of SMC against bounded exogenous disturbances. Additionally, the SMC reaching law in the proposed control scheme is augmented with a nonlinear adaptation mechanism that flexibly modulates the control activity to effectively compensate for the external perturbations while minimizing the chattering content. The controller parameters are numerically optimized offline. The efficacy of the prescribed hybrid control law is analyzed via customized MATLAB simulations that normalize the patient's BG level to 80 mg/dL, under measurement noise and meal disruptions, from an initial hyperglycemic state. The results justify the improved BG regulation accuracy and disturbance-rejection capability of the proposed control procedure.