Measures and LMIs for Impulsive Nonlinear Optimal Control

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00217550" target="_blank" >RIV/68407700:21230/14:00217550 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TAC.2013.2292735" target="_blank" >http://dx.doi.org/10.1109/TAC.2013.2292735</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TAC.2013.2292735" target="_blank" >10.1109/TAC.2013.2292735</a>

Result language
angličtina
Original language name
Measures and LMIs for Impulsive Nonlinear Optimal Control
Original language description
This note shows how to use semi-definite programming to find lower bounds on a large class of nonlinear optimal control problems with polynomial dynamics and convex semialgebraic state constraints and an affine dependence on the control. This is done byrelaxing an optimal control problem into a linear programming problem on measures, also known as a generalized moment problem. The handling of measures by their moments reduces the problem to a convergent series of standard linear matrix inequality relaxations. When the optimal control consists of a finite number of impulses, we can recover simultaneously the actual impulse times and amplitudes by simple linear algebra. Finally, our approach can be readily implemented with standard software, as illustrated by a numerical example.
Czech name
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Czech description
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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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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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