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Estimation and optimal input design in sparse models

Time: Thu 2023-09-28 15.15

Location: D3, Lindstedtsvägen 5, Stockholm

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Language: English

Subject area: Electrical Engineering

Doctoral student: Javad Parsa , Reglerteknik

Opponent: Associate Professor Kim Batselier, Delft University of Technology, Netherlands

Supervisor: Professor Håkan Hjalmarsson, Reglerteknik

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QC 20230911


Sparse parameter estimation is an important aspect of system identification, as it allows for reducing the order of a model, and also some models in system identification inherently exhibit sparsity in their parameters. The accuracy of the estimated sparse model depends directly on the performance of the sparse estimation methods. It is well known that the accuracy of a sparse estimation method relies on the correlations between the regressors of the model being estimated. Mutual coherence represents the maximum of these correlations. When the parameter vector is known to be sparse, accurate estimation requires a low mutual coherence.

However, in system identification, a major challenge arises from the construction of the regressor based on time series data, which often leads to a high mutual coherence. This conflict hinders accurate sparse estimation. To address this issue, the first part of this thesis introduces novel methods that reduce mutual coherence through linear coordinate transformations. These methods can be integrated with any sparse estimation techniques. Our numerical studies demonstrate significant improvements in performance compared to state-of-the-art sparse estimation algorithms.

In the second part of the thesis, we shift our focus to optimal input design in system identification, which aims to achieve maximum accuracy in a model based on specific criteria. The original optimal input design techniques lack coherence constraints between the input sequences, often resulting in high mutual coherence and, consequently, increased sparse estimation errors for sparse models. Therefore, the second part of the thesis concentrates on designing optimal input for sparse models. We formulate the proposed methods and propose numerical algorithms using alternating minimization. Additionally, we compare the performance of our proposed methods with state-of-the-art input design algorithms, and we provide theoretical analysis of the proposed methods in both parts of the thesis.