Nonzero Bound on Fiedler Eigenvalue Causes Exponential Growth of H-Infinity Norm of Vehicular Platoon
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F15%3A00231632" target="_blank" >RIV/68407700:21230/15:00231632 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TAC.2014.2366980" target="_blank" >http://dx.doi.org/10.1109/TAC.2014.2366980</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TAC.2014.2366980" target="_blank" >10.1109/TAC.2014.2366980</a>
Alternative languages
Result language
angličtina
Original language name
Nonzero Bound on Fiedler Eigenvalue Causes Exponential Growth of H-Infinity Norm of Vehicular Platoon
Original language description
We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differentlyby the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix?the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H-infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Automatic Control
ISSN
0018-9286
e-ISSN
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Volume of the periodical
60
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
2248-2253
UT code for WoS article
000358642500026
EID of the result in the Scopus database
2-s2.0-84938374791