DocumentCode :
115168
Title :
Approximate regularization path for nuclear norm based H2 model reduction
Author :
Blomberg, Niclas ; Rojas, Cristian R. ; Bo Wahlberg
Author_Institution :
KTH R. Inst. of Tech, Stockholm, Sweden
fYear :
2014
fDate :
15-17 Dec. 2014
Firstpage :
3637
Lastpage :
3641
Abstract :
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model reduction problem as a function of the design parameter. This is called the regularization path in sparse estimation and is a very important tool in order to find the appropriate balance between fit and complexity. We extend this to the more complicated nuclear norm case. The key idea is to determine when to exactly calculate the optimal solution using an upper bound based on the so-called duality gap. Hence, by solving a fixed number of optimization problems the whole regularization path up to a given tolerance can be efficiently computed. We illustrate this approach on some numerical examples.
Keywords :
convex programming; matrix algebra; reduced order systems; Hankel matrix; approximate regularization path; convex optimization problem; duality gap; dynamical systems; model complexity; model fit; model reduction problem; optimization problems; sparse estimation; Approximation algorithms; Approximation error; Minimization; Reduced order systems; Upper bound; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on
Conference_Location :
Los Angeles, CA
Print_ISBN :
978-1-4799-7746-8
Type :
conf
DOI :
10.1109/CDC.2014.7039955
Filename :
7039955
Link To Document :
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