Abstract:
The inverse problem of identifying unknown parameters of known structure dynamical biological systems, which are
modelled by ordinary differential equations or delay differential equations, from experimental data is treated in this paper. A two stage
approach is adopted: first, combine spline theory and Nonlinear Programming (NLP), the parameter estimation problem is formulated
as an optimization problem with only algebraic constraints; then, a new differential evolution (DE) algorithm is proposed to find a
feasible solution. The approach is designed to handle problem of realistic size with noisy observation data. Three cases are studied to
evaluate the performance of the proposed algorithm: two are based on benchmark models with priori-determined structure and
parameters; the other one is a particular biological system with unknown model structure. In the last case, only a set of observation
data available and in this case a nominal model is adopted for the identification. All the test systems were successfully identified by
using a reasonable amount of experimental data within an acceptable computation time. Experimental evaluation reveals that the
proposed method is capable of fast estimation on the unknown parameters with good precision.
