Publication

Enhancing statistical performance of data-driven controller tuning via L2-regularization

Alireza Karimi
2014
Journal Articles

Abstract

Noniterative data-driven techniques are design methods that allow optimal feedback control laws to be derived from input-output (I/O) data only, without the need of a model of the process. A drawback of these methods is that, in their standard formulation, they are not statistically efficient. In this paper, it is shown that they can be reformulated as L2-regularized optimization problems, by keeping the same assumptions and features, such that their statistical performance can be enhanced using the same identification data set. A convex optimization method is also introduced to find the regularization matrix. The proposed strategy is finally tested on a benchmark example in digital control system design.

Official source

https://infoscience.epfl.ch/entities/publication/826fbeaa-7742-4a70-af1e-2f5d7ded2fa6

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Alireza Karimi
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/826fbeaa-7742-4a70-af1e-2f5d7ded2fa6

About this result

Related concepts (32)

Regularization (mathematics)

In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.

Ridge regression

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.

Elastic net regularization

In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on Use of this penalty function has several limitations. For example, in the "large p, small n" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates.

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