On the Optimality of Open and Closed Loop Experiments in System Identification

In this paper we analyse the strong optimality of open and closed loop experiments. In particular, we establish that when there is a constraint on the system input, then open loop experiments are optimal for a wide class of design criteria. Conversely, we show that when there is a constraint on the output power, then closed loop experiments are optimal for a class of systems and for a wide class of design criteria. Our analysis uses the non-asymptotic (in model order) variance expressions for dynamic systems