Design of Luenberger Observer for Glucose-Insulin Control via Mathematica

Many articles dealing with insulin-glucose control have been published in the last decades, and they mostly assumed that all the system state variables are available for feedback. However, this is not usually the case, or they are not so cheap in practice as blood glucose measurements are. In this paper the use of the reduced-order estimator (also known as the Luenberger observer) is considered in symbolic form employing polynomial control system application of mathematica for the three-state minimal Bergman model, as this can be used to reconstruct those state variables that are hard to be recovered directly from the system outputs: remote compartment insulin and plasma insulin. Nonlinear closed loop simulations with H₂/H_infin control (disturbance rejection LQ method) showed that the observer, which is faster than the system itself, can provide a very good state recovery performance.