  A model-based optimal experiment design (OED) of nonlinear systems is
studied. OED represents a methodology for optimizing the geometry of the
parametric joint-confidence regions (CRs), which are obtained in an a
posteriori analysis of the least-squares parameter estimates. The optimal
design is achieved by using the available (experimental) degrees of freedom
such that more informative measurements are obtained. Unlike the commonly used
approaches, which base the OED procedure upon the linearized CRs, we explore a
path where we explicitly consider the exact CRs in the OED framework. We use a
methodology for a finite parametrization of the exact CRs within the OED
problem and we introduce a novel approximation technique of the exact CRs using
inner- and outer-approximating ellipsoids as a computationally less demanding
alternative. The employed techniques give the OED problem as a
finite-dimensional mathematical program of bilevel nature. We use two
small-scale illustrative case studies to study various OED criteria and compare
the resulting optimal designs with the commonly used linearization-based
approach. We also assess the performance of two simple heuristic numerical
schemes for bilevel optimization within the studied problems.
