Integrating Parameter Selection with Experimental Design under Uncertainty for Nonlinear Dynamic Systems

Models describing complex processes often contain a large number of parameters as part of the nonlinear 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 values depend on assumed values of the parameters and initial states, as well as known trajectories of the input signals.

In this work parameter selection and experiment design procedures are integrated into a unified framework which optimizes a criterion of the Fisher information matrix and simultaneously takes the effect of uncertainty in the parameter values into account. A hybrid method combining a genetic algorithm and a simultaneous perturbation stochastic approximation is developed to solve the resulting mixed-integer nonlinear programming problem. The technique is illustrated on a model of a CSTR and of a signal transduction pathway.