Convex Computation of the Region of Attraction of Polynomial Control Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00214843" target="_blank" >RIV/68407700:21230/14:00214843 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TAC.2013.2283095" target="_blank" >http://dx.doi.org/10.1109/TAC.2013.2283095</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TAC.2013.2283095" target="_blank" >10.1109/TAC.2013.2283095</a>
Alternative languages
Result language
angličtina
Original language name
Convex Computation of the Region of Attraction of Polynomial Control Systems
Original language description
We address the long-standing problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We show that the ROA can be computed by solving an infinite-dimensional convex linear programming (LP) problem over the space of measures. In turn, this problem can be solved approximately via a classical converging hierarchy of convex finite- dimensional linear matrix inequalities (LMIs). Our approach is genuinely primal in the sense that convexity of the problem of computing the ROA is an outcome of optimizing directly over system trajectories. The dual infinite-dimensional LP on nonnegative continuous functions (approximated by polynomial sum-of-squares) allows us to generate a hierarchy of semialgebraic outer approximations of the ROA at the price of solving a sequence of LMI problems with asymptotically vanishing conservatism. This shar
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
<a href="/en/project/GA13-06894S" target="_blank" >GA13-06894S: Semidefinite programming for polynomial optimal control problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
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
59
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
297-312
UT code for WoS article
000330767500002
EID of the result in the Scopus database
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