Planning of harmonic input signals in the problem of dynamic system identification

The task of planning optimal harmonic input signals in the problem of the identification of linear stationary dynamic systems with a single input and a vector output subject to restrictions on the characteristics of input and output signals is considered. To solve this problem, the frequency-time approach is applied: an input signal is formed in a specified frequency band and on large time intervals. The optimality of the input signals is treated in the sense of the criteria of D-, E-, and L-optimality employed in the theory of experimental design. The process of planning optimal harmonic input signals is reduced to a problem of nonlinear mathematical programming. The comparison of the optimal and harmonic input signals is illustrated by informative numerical examples.