A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal...

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Veröffentlicht in:Automatica (Oxford) 1992-09, Vol.28 (5), p.897-909
Hauptverfasser: Spanos, J.T., Milman, M.H., Mingori, D.L.
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Milman, M.H.
Mingori, D.L.
description In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.
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subjects Applied sciences
Computer science
control theory
systems
Control theory. Systems
Cybernetics
Exact sciences and technology
least-squares approximations
Model reduction
Optimal control
optimization
title A new algorithm for L2 optimal model reduction
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