Identification for control: some results on optimal experiment design

The problem of designing identification experiments to make them maximally informative with respect to the intended use of the model is studied. Focus is on model based control and we show how to choose the feedback regulator and the spectrum of the reference signal in case of closed-loop experiments. A main result is that when only the misfit in the dynamics model is penalized and when both the input and the output power are constrained then the optimal controller is given by the solution to a standard LQ problem. When only the input power is constrained, it is shown that open-loop experiments are optimal. Some examples are also given to exemplify the theoretical results