# Identification of low-order models using rational orthonormal basis functions

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Abstract

A method for complexity constrained output-error system identification using rational orthonormal basis functions is presented. The model is expanded in terms of a Hambo basis, which generalizes several well-known bases such as the natural basis, Laguerre and Kautz basis. Properties of the Hambo operator transform induced by the basis functions are used to constrain the model order in the operator domain. The identification problem is formulated as a rank-constrained least-squares minimization problem, which is relaxed using the nuclear-norm to form a convex optimization problem. We demonstrate on a numerical example that the proposed identification method can outperform other state-of-the-art methods which rely on model order reduction to obtain low-order models.A method for complexity constrained output-error system identification using rational orthonormal basis functions is presented. The model is expanded in terms of a Hambo basis, which generalizes several well-known bases such as the natural basis, Laguerre and Kautz basis. Properties of the Hambo operator transform induced by the basis functions are used to constrain the model order in the operator domain. The identification problem is formulated as a rank-constrained least-squares minimization problem, which is relaxed using the nuclear-norm to form a convex optimization problem. We demonstrate on a numerical example that the proposed identification method can outperform other state-of-the-art methods which rely on model order reduction to obtain low-order models.