CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR 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%3A00220940" target="_blank" >RIV/68407700:21230/14:00220940 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/130914565" target="_blank" >http://dx.doi.org/10.1137/130914565</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/130914565" target="_blank" >10.1137/130914565</a>
Alternative languages
Result language
angličtina
Original language name
CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR POLYNOMIAL CONTROL SYSTEMS
Original language description
We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialgebraic state and control constraints, we describe a hierarchy of finite-dimensional linear matrix inequality (LMI) relaxations whose optimal values converge to the volume of the MCI set; dual to these LMI relaxations are sum-of-squares (SOS) problems providing a converging sequence of outer approximations to the MCI set. The approach is simple and readily applicable in the sense that the approximations are the outcome of a single semidefinite program with no additional input apart from the problem description. A number of numerical examples illustrate the approach.
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
SIAM Journal on Control and Optimization
ISSN
0363-0129
e-ISSN
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Volume of the periodical
52
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
2944-2969
UT code for WoS article
000344748000012
EID of the result in the Scopus database
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