Geometric adaptive control in type 1 diabetes

Abstract

In geometric control model based methods, it is well known that if a nonlinear system has its relative degree equal to the number of states in the neighborhood of a point of equilibrium, thus it is possible to perform a coordinate transformation and a state feedback that transforms the nonlinear system into a linear and controllable one. Stabilization of this system is possible by a simple linear control technique. This method is based on the exact cancellation of nonlinear terms. If the parameters are either time-varying or there is uncertainty in the nonlinear terms of the model, then cancellation would not be longer accurate. The modification of the control method with adaptive parameters, makes asymptotically exact the cancellation of the nonlinear terms and maintains the efficiency of the transformation. This paper presents a nonlinear adaptive control method based on exact linearization techniques applied to the automation of blood glucose regulation in Type-1 diabetes. Using continuous blood glucose monitoring as the input, the method provides the insulin infusion function as the output. Since the insulin infusion calculated drives blood glucose to normal levels, the method mimics the healthy pancreas function and it could be applied in artificial pancreas to control blood glucose in type 1 diabetic patients.