Assessment of performance limitations due to nonlinearity in a model of a human with diabetes

A 19/sup th/-order in silico patient model is analyzed to determine if nonlinear control is necessary for optimal regulation of blood glucose levels. A numerical measure of nonlinearity is used to assess the open-loop degree of nonlinearity and the results then compared to those from an assessment of the control-relevant nonlinearity. Control-relevant nonlinearity is assessed with a performance metric that uses the system´s nonlinear closed-loop operators to calculate bounds on the achievable performance of stabilizing, linear control designs. The results show that the open-loop system is mildly nonlinear in a typical operating region and has a low degree of control-relevant nonlinearity for standard, linear performance specifications. If asymmetric performance is desired, in which negative deviations are rejected more aggressively than positive deviations, the control-relevant nonlinearity grows significantly indicating that nonlinear control is necessary to achieve this task optimally. The results indicate that the primary contributor to the control-relevant nonlinearity is the performance objective and that, for most cases, linear control is sufficient for blood glucose regulation.