In the first part of this paper, the problem of using an uncertain pharmacokinetic model is resolved to determine drug concentrations in rats after the oral administration of drug suspensions with and without added tenside. To this end, a generalized pharmacokinetic model determining the guaranteed limits of drug concentrations was designed. Based on this, the design of the so-called state-bounding observer is described in the second part. Rather than being driven by the output of the pharmacokinetic model, the observer can be driven exclusively by a concentration collected from a suitable part of the body and predict the possible risk of the drug concentration not remaining within the therapeutic range for a sufficiently long time. Specifically, the observer determines the upper and lower limits of the concentrations in all the compartments, especially those that are inaccessible for the collection of samples. The proposed approaches are demonstrated by examples.

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The error of single step-ahead output prediction is the information traditionally used to correct the state estimate while exploiting the new measurement of the system output. However, its dynamics and statistical properties can be further studied and exploited in other ways. It is known that in the case of suboptimal state estimation, this output prediction error forms a correlated sequence, hence it can be effectively predicted in real time. Such a suboptimal scenario is typical in applications where the process noise model is not known or it is uncertain. Therefore, the paper deals with the problems of analytical and empirical modeling, identification, and prediction of the output error of the suboptimal state estimator for the sake of improving the output prediction accuracy and ultimately the performance of the model predictive control. The improvements are validated on an empirical model of type 1 diabetes within an in-silico experiment focused on glycemia prediction and implementation of the MPC-based artificial pancreas.