Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00184746" target="_blank" >RIV/68407700:21230/11:00184746 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations
Original language description
Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximation of its solution. In a second step we apply maximum entropy estimation (using moments of aBorel measure associated with the discrete solution) to obtain a smooth closed-form approximation. The approach is illustrated on a variety of linear and nonlinear ordinary differential equations (ODE), partial differential equations (PDE) and optimal control problems (OCP), and preliminary numerical results are reported.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 18th IFAC World Congress, 2011
ISBN
978-3-902661-93-7
ISSN
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e-ISSN
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Number of pages
6
Pages from-to
10887-10892
Publisher name
IFAC
Place of publication
Bologna
Event location
Milano
Event date
Aug 28, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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