Interval Tools for ODEs and DAEs
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Rigorous integration of flows and ODEs using taylor models
Proceedings of the 2009 conference on Symbolic numeric computation
SQualTrack: a tool for robust fault detection
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets
Automatica (Journal of IFAC)
Computer Methods and Programs in Biomedicine
Computer Methods and Programs in Biomedicine
Guaranteed computation methods for compartmental in-series models under uncertainty
Computers & Mathematics with Applications
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Insulin therapy in type 1 diabetes aims to mimic the pattern of endogenous insulin secretion found in healthy subjects. Glucose-insulin models are widely used in the development of new predictive control strategies in order to maintain the plasma glucose concentration within a narrow range, avoiding the risks of high or low levels of glucose in the blood. However, due to the high variability of this biological process, the exact values of the model parameters are unknown, but they can be bounded by intervals. In this work, the computation of tight glucose concentration bounds under parametric uncertainty for the development of robust prediction tools is addressed. A monotonicity analysis of the model states and parameters is performed. An analysis of critical points, state transformations and application of differential inequalities are proposed to deal with non-monotone parameters. In contrast to current methods, the guaranteed simulations for the glucose-insulin model are carried out by considering uncertainty in all the parameters and initial conditions. Furthermore, no time-discretisation is required, which helps to reduce the computational time significantly. As a result, we are able to compute a tight glucose envelope that bounds all the possible patient's glycemic responses with low computational effort.