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Optimization Methods for Novel System Identification Techniques (Hankel Matrix Nuclear Norm Minimization via the Alternating Direction Method of Multipliers)


V. Semeraro

Master Thesis, HS12 (10276)

In this master thesis project we address well-known issues of the classical frequency domain subspace identification method for uniformly spaced frequency response samples. Nuclear norm based optimization methods are shown to be a promising alternative to the classical approach, but have been applied to general solvers so far. We develop and implement specialized algorithms for the Hankel matrix nuclear norm minimization subject to convex constraints, which arise in system identification problems. For this purpose we consider well-known reformulations of the nuclear norm based optimization problem. A Newton method using logarithmic barrier functions based on the semi-definite program formulation subject to bounded noise energy is presented and implemented. Alternatively, we also provide an alternating direction method of multipliers (ADMM) for solving the Hankel matrix nuclear norm minimization subject to bounded noise energy and bounded noise cumulative spectrum. The latter is a more realistic constraint in a system identification setting, since it assigns white-noise characteristics to the sought solution. We compare and evaluate the performance of the two approaches and determine which one is more suitable for system identification. In addition, we present two alternative ADMM approaches for solving the optimization problem subject to a bounded cumulative spectrum constraint. For this case we also provide an analysis and determine which approach performs better. A performance comparison of ADMM with a general solver is also presented. Finally, an application to system identification using ADMM for the estimation of a linear MIMO-system concludes this thesis.


Type of Publication:

(12)Diploma/Master Thesis

R. S. Smith

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2013:IFA_4492
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