On the Observation of Glucose–Insulin Models

Abstract The glucose–insulin subsystem has been modeled in different ways as a low‐dimensional dynamical system. These models consist of various parameters, which are fitted such that the model coincides with specific experiments. For individuals with the Diabetes Mellitus syndrome model‐based controllers for insulin injection have been proposed. These controllers, however, require the knowledge of the model parameters as well as the full systems state, which must be estimated as well. In addition, the system is disturbed by, in general, unknown carbohydrate intake. From a control‐theoretic point of view, the state estimation using only the measurable glucose concentration is an observer problem. Due to the nonlinearity of the system, its observability is more difficult to test. There may also be some points in the state space, where the system is not locally observable for some parameters tuples. Those issues are important for a robust observer design. In this contribution, several observers are discussed for the widely used Bergman minimal model. These include unknown‐input observers that make use of the special systems structure as well as observers based on the observability canonical form with different embedding dimensions. The canonical form is computed by algebraic methods.