Robustness Aspects in Parameter Estimation, Optimal Design of Experiments and Optimal Control

Summary Estimating model parameters from experimental data is crucial to reliably simulate dynamic processes. In practical applications, however, it often appears that the data contains outliers. Thus, a reliable parameter estimation procedure is necessary that delivers parameter estimates insensitive (robust) to errors in measurements. Another difficulty that occurs in practical applications is that the experiments performed to obtain measurements for parameter estimation are expensive, but nevertheless do not guarantee satisfactory parameter accuracy. The optimization of one or more dynamic experiments in order to maximize the accuracy of the results of a parameter estimation subject to cost and further technical inequality constraints leads to very complex non-standard optimal control problems. Newly developed successful methods and software for design of optimal experiments for nonlinear processes are based on the expansion of the problem at the nominal value of parameters which lie in a (possibly large) confidence region. Robust optimal experiments, that are insensitive against uncertainties in parameter values, should be obtained if we optimize the experiments in min-max fashion (worst-case design) over the whole range (confidence region) of an uncertainty set. The paper presents new effective algorithms for robust parameter estimation and design of robust optimal experiments in dynamic systems. Numerical results for a real-life application from biochemical engineering are presented.