Glucose optimal control system in diabetes treatment

Abstract Optimal control allows the incorporation of functional constraints and requirements as a departure point for the design process. A control system for optimal insulin delivery in a type I diabetic patient is presented based on the linear quadratic control problem theory. The glucose–insulin dynamics is first represented by a linear model whose state variables are the glucose and the insulin concentrations in the blood. These variables allow the formulation of an appropriate cost function for a diabetes treatment in terms of the deviation from the normal glucose level and the dosage of exogenous insulin. The optimal control law is computed from this cost function under the servocontrol and regulatory approaches. A Monte Carlo simulation shows the superior robustness of the regulatory control design. Further evaluation of the regulatory controller is realized with a high order non-linear human glucose–insulin model. The control system performance can be improved by adjusting the weighting factors of the optimization problem according to the patient’s needs. The velocity of the correction of a glucose level deviation can be increased with a higher value for its weighting factor, while an augment of the weighting factor for insulin supply may be necessary to prevent saturation of the controller output and oscillation of the blood glucose concentration. Results exemplify the suitability of the optimization and regulatory approaches to produce a practical control algorithm for biomedical engineering problems.