ON OPTIMAL INPUT DESIGN IN SYSTEM IDENTIFICATION1

System identification concerns the construction and validation of mathematical models of dynamical systems from experimental data. The objective of this contribution is to discuss new research directions in experiment design , e.g. how to design informative experiments which satisfy specifications on the resulting model quality and practical limitations such as constraints on input and output signals, but also experimental time. In particular, we discuss how input design is instrumental for alleviating the problem of modelling complex systems. Many optimal experiment design problems can be formulated as optimal control problems, but with nonstandard cost functions. A difficulty is that the solution often depends on the true system. To solve optimal control problems, we can exploit recent advances in numerical optimization for control design, including convex optimization and relaxation methods. As a more concrete example, we study how to estimate the ℋ∞ norm of a system.