On the choice of inputs in identification for robust control
The authors deal with identification in the sense of estimating the coefficients of the numerator and denominator polynomials of a rational transfer function when noisy measurements of both the input and output of the system with this transfer function are known. They begin with the review of the classical approach to design optimal inputs for identification. They also study the identification problem for robust control on the assumption that an upper bound on the norm of the perturbation affecting the data is a priori known. Thus, the second-smallest eigenvalue of an appropriate defined data covariance matrix is a quantity which provides an upper bound for the size of the uncertainty affecting the data. Further it is shown that the problem of computing optimal inputs, reformulated in the frequency domain, is equivalent to a linear matrix inequality problem. For a linear, time-invariant, discrete-time system, an optimal input is designed which maximizes the second-smallest singular value of the data matrix defined in a certain way. Also, the stationary points of the eigenvalues of a certain data covariance matrix \(\mathcal D\) are computed explicitly in terms of the coefficients of the numerator and denominator of the transfer function; this leads to upper and lower bounds of the second-smallest singular value \(\sigma_*\) of \(\mathcal D\). Finally, the results of a simulation experiment are presented comparing the random input with the input obtained by the above-mentioned optimization and the inverse optimal-input problem is discussed.
scientific article; zbMATH DE number 1331907