Computation of Optimal Identification Experiments for Nonlinear Dynamic Process Models: a Stochastic Global Optimization Approach

Abstract

The problem of optimal experimental design (OED) for parameter estimation of nonlinear dynamic systems is considered. It is shown how this problem can be formulated as a dynamic optimization (optimal control) problem where the performance index is usually a scalar function of the Fisher information matrix. Numerical solutions can be obtained using direct methods, which transform the original problem into a nonlinear programming (NLP) problem via parametrizations. However, because of the frequent nonsmoothness of the cost functions, the use of gradient-based methods to solve this NLP might lead to local solutions. Stochastic methods of global optimization are suggested as robust alternatives. A case study considering the OED for parameter estimation in a fed-batch bioreactor is used to illustrate the performance and advantages of two selected stochastic algorithms.