Abstract
Design of optimal input excitations is one of the most challenging problems in the field of system identification. The main difficulty lies in the fact that the optimization problem cannot always be formulated to be convex, therefore a globally optimal excitation for the dynamic system of interest cannot be guaranteed. In this paper, optimal input design (OID) for linear systems in the presence of prior knowledge is studied. Information related to exponential decay and smoothness is incorporated in the optimal input design problem by making use of the Bayes rule of information. Three different cases of modeling the linear dynamics are considered, namely Finite Impulse Response (FIR) model with and without prior knowledge, as well as the rational transfer function case. It is shown that the prior information affects the spectrum of the minimum power optimal input. The input with the least power is always obtained for the transfer function model case.
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