Selection of Parameter Sets and Design of Experiments for Estimation of Nonlinear Dynamic Systems

Models describing complex processes often contain a large number of parameter and may need to describe nonlinear behavior of the system. It is usually not possible in practice to identify all parameters due to the number and quality of measurement data as well as interactions among the parameters. A common approach is to select a set of parameters for estimation while other parameters are fixed at their nominal values. Such a parameter selection procedure is often based on sensitivity analysis; however, the determined sensitivity value depends on an assumed distribution of values of the parameters, initial states and known trajectories of the input signals. This work addresses some of the mentioned issues and presents a procedure which combines parameter selection for estimation with experimental design. Additionally, the effect that uncertainty in the parameter values has on the parameter set selection is also taken into account. An optimization problem is formulated whose solution is the optimal set of parameters to be estimated and the experimental conditions required for determining this set of parameters.