On optimal experiment design for parameters estimation of dynamic systems under periodic operation

This paper deals with the parameters estimation of a discrete-time and time - invariant system affected by additive output noise, under periodic operation. Assuming a norm of the Fisher Information Matrix as performance index, the problems of the optimal periodic input design, of the joint optimal periodic input and measurement schedules design and of the choice of the best period for parameters estimation are formally stated. Through the introduction of the Fisher per sample Information Matrix, they are recognized as Periodic Optimal Control problems. A closed form solution is found in the particular case of linear systems with a scalar unknown parameter.