SIAM Journal on Control and Optimization
Closed loop experiment design for linear time invariant dynamical systems via LMIs
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Least costly identification experiment for control
Automatica (Journal of IFAC)
Technical Communique: Asymptotic variance expressions for closed-loop identification
Automatica (Journal of IFAC)
On the frequency domain accuracy of closed-loop estimates
Automatica (Journal of IFAC)
Kullback-Leibler approximation of spectral density functions
IEEE Transactions on Information Theory
Relative entropy and the multivariable multidimensional moment problem
IEEE Transactions on Information Theory
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We investigate how the variance error associated with the prediction error identification is related to the power spectral densities of the input and the additive noise at the output. Let @F(e^i^@w) be the ratio of the input power spectral density (PSD) to the output-noise PSD. We characterize the set of all functions @F for which the variance error remains constant. This analysis results a minimal, finite-dimensional, affine parameterization of the variance error. This parameterization connects our analysis with the theory of Nevanlinna-Pick interpolation. It is shown that the set of all @F for which the variance error remains constant can be characterized by the solutions of a Nevanlinna-Pick interpolation problem. This insight has interesting consequences in optimal input design, where it is possible to use some recent tools in analytic interpolation theory to tune shape of the input PSD to suit certain needs.