On the Parameter Estimation for Compartment Models with Uncertain Data
Evgenija D. Popova · 2016
interval data, parametric interval linear systems. Consider a mammillary model with one central compartment commu-nicating with p − 1 peripheral compartments. The solution of the homoge-neous system of the governing equations is given by f(x, t) = p∑ j=1 x2j−1 exp(−x2jt), x ∈ Rn, n = 2p. The goal is to estimate the set of all parameter values (amplitudes x2j−1 and decay constants x2j, j = 1,..., p), which are consistent with the ob-servations ỹi contained in given intervals [yi, yi], that is yi ≤ f(x, ti) ≤ yi, i = 1,...,m. The methodology for guaranteed parameter set estimation of exponential sums, proposed in [1], is based on Prony’s method for interval-valued data. Since exponential sums may be very sensitive to changes in their parameters, special emphasis is put on finding sharp bounds for the