Large-scale minimization of the pseudospectral abscissa

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21220%2F24%3A00381205" target="_blank" >RIV/68407700:21220/24:00381205 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1137/22M1517329" target="_blank" >https://doi.org/10.1137/22M1517329</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/22M1517329" target="_blank" >10.1137/22M1517329</a>

Result language

angličtina

Original language name

Large-scale minimization of the pseudospectral abscissa

Original language description

This work concerns the minimization of the pseudospectral abscissa of a matrixvalued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control system that has optimization parameters. We describe a subspace procedure to cope with the setting when the matrix-valued function is of large size. The proposed subspace procedure solves a sequence of reduced problems obtained by restricting the matrix-valued function to small subspaces, whose dimensions increase gradually. It possesses desirable features such as a superlinear convergence exhibited by the decay in the errors of the minimizers of the reduced problems. In mathematical terms, the problem we consider is a large-scale nonconvex minimax eigenvalue optimization problem such that the eigenvalue function appears in the constraint of the inner maximization problem. Devising and analyzing a subspace framework for the minimax eigenvalue optimization problem at hand with the eigenvalue function in the constraint require special treatment that makes use of a Lagrangian and dual variables. There are notable advantages in minimizing the pseudospectral abscissa over maximizing the distance to instability or minimizing the 7-tinfty norm; the optimized pseudospectral abscissa provides quantitative information about the worst-case transient growth, and the initial guesses for the parameter values to optimize the pseudospectral abscissa can be arbitrary, unlike the case to optimize the distance to instability and 7-tinfty norm that would normally require initial guesses yielding asymptotically stable systems.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20205 - Automation and control systems

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

1095-7162

Volume of the periodical

45

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

31

Pages from-to

2104-2134

UT code for WoS article

001343416000015

EID of the result in the Scopus database

2-s2.0-85207945198