On the Optimality of Binary-Open-Loop Experiments to Identify Hammerstein Systems

This paper analyzes optimal experiment design for Hammerstein models. We show that, under general conditions, open loop experiments are optimal when one constrains the system input, and also for a specific class of systems when there is a constraint on the output power. Furthermore, we analyze an experiment which uses a binary signal, and show it to be optimal when the system is in open loop. Both results use a strong notion of optimality and expressions for estimation accuracy which are non-asymptotic in model order and asymptotic in data length. We also develop a procedure to design an experiment which uses binary input signals based on semi-definite programming.