Model-based design of optimal experiments for nonlinear systems in the context of guaranteed parameter estimation

An approach to the design of experiments is presented in the framework of bounded-error (guaranteed) parameter estimation for nonlinear static and dynamic systems. The guaranteed parameter estimation determines non-asymptotic confidence limits on the unknown parameters of a mathematical model. An essential part of the solution procedure is the approximation of the joint-confidence region. In this contribution, we develop and analyze the procedure and different ways of achieving a tight over-approximation of the solution set of guaranteed parameter estimation based on the expected values of parameters. Finally we propose to solve the problem of the design of experiments as a bilevel program. We demonstrate our approach and analyze the nature of the problem in the static and dynamic case studies. The proposed approach is also compared to the experiment design in the context of least-squares estimation and to the linearization-based techniques for optimal experiment design proposed in the literature earlier.