Simulation of Uncertain Dynamic Systems Described by Interval Models: A Survey

Puig, Vicenç; Stancu, Alexandru; Quevedo, Joseba

doi:10.3182/20050703-6-cz-1902.00208

Cited by 17 publications

(31 citation statements)

References 39 publications

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“…Such a computation can be performed by using one-step-ahead iteration based on previous approximations of the reachable set (region-based approaches), or a set of point-wise trajectories generated by the selection of particular values of the parameters p ∈ p and initial conditions x 0 ∈ x 0 by using heuristics or optimisation (trajectory-based approaches) [9]. Algorithms to compute solution envelopes are classified according to the type of approach.…”

Section: Initial Value Problems For Parametric Odesmentioning

confidence: 99%

“…This produces an overestimation commonly known as the wrapping effect [9,10]. Regions must be feasible to be constructed and represented on a computer, or the region representation will produce a significant overestimation.…”

Section: Region-based Approachesmentioning

confidence: 99%

“…First of all, the non-insulindependent glucose disposal (8) and the renal glucose clearance (9) are transformed such that F c [6], where…”

Section: The Glucose Metabolism Systemmentioning

confidence: 99%

See 2 more Smart Citations

On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

Pereda

Romero‐Vivó

Ricarte

et al. 2012

Computer Methods and Programs in Biomedicine

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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.

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Section: Initial Value Problems For Parametric Odesmentioning

confidence: 99%

Section: Region-based Approachesmentioning

confidence: 99%

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On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

Pereda

Romero‐Vivó

Ricarte

et al. 2012

Computer Methods and Programs in Biomedicine

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“…The monotonicity of the system with respect to the parameters of the model can be analysed by considering the parameters as system states in an extended model [3], that is, by performing a monotonicity analysis of a new system with n + n p states given by:…”

Section: Uncertain Systemsmentioning

confidence: 99%

“…Trajectory-based approaches have been also applied to obtain solution envelopes [3][4][5]. Compared with Monte Carlo simulations, monotonicity analysis guarantees that the actual response is inside the envelopes.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed computation methods for compartmental in-series models under uncertainty

Pereda

Romero‐Vivó

Ricarte

et al. 2013

Computers & Mathematics with Applications

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The pattern of some real phenomenona can be described by compartmental in-series models. Nevertheless, most of these processes are characterized by their variability, which produces that the exact values of the model parameters are uncertain, although they can be bounded by intervals.The aim of this paper is to compute tight solution envelopes that guarantee the inclusion of all possible behaviours of such processes. Current methods, such as monotonicity analysis, enable us to obtain guaranteed solution envelopes. However, if the model includes non-monotone compartments or parameters, the computation of solution envelopes may produce a significant overestimation.Our proposal consists in performing a change of variables in which the output is unaltered, and the model obtained is monotone with respect to the uncertain parameters. The monotonicity of the new system allows us to compute the output bounds for the original system without overestimation. These model transformations have been developed for linear and non-linear systems. Furthermore, if the conditions are not completely satisfied, a novel method to compute tight solution envelopes is proposed. The methods exposed in this paper have been applied to compute tight solution envelopes for two different models: a linear system for glucose modelling and a non-linear system for an epidemiological model.

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Physiology-Based Interval Models: A Framework for Glucose Prediction Under Intra-patient Variability

Bondia

Vehı́

2015

Lecture Notes in Bioengineering

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Simulation of Uncertain Dynamic Systems Described by Interval Models: A Survey

Cited by 17 publications

References 39 publications

On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

Guaranteed computation methods for compartmental in-series models under uncertainty

Physiology-Based Interval Models: A Framework for Glucose Prediction Under Intra-patient Variability

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