Abstract
The pattern of some real phenomenon 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 behaviors of such processes. Current methods, such as monotonicity analysis,
enable us to obtain guaranteed solution envelopes. However, if the model includes nonmonotone
compartments or parameters, the computation of solution envelopes may
produce a significant overestimation.
Our proposal consists of 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 modeling and a non-linear system for an
epidemiological model.
