En Route for the Calculus of Variations
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F01801376%3A_____%2F19%3AN0000001" target="_blank" >RIV/01801376:_____/19:N0000001 - isvavai.cz</a>
Výsledek na webu
<a href="http://eiris.it/ojs/index.php/ratiomathematica/issue/view/36-2019" target="_blank" >http://eiris.it/ojs/index.php/ratiomathematica/issue/view/36-2019</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.23755/rm.v36i1.467" target="_blank" >10.23755/rm.v36i1.467</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
En Route for the Calculus of Variations
Popis výsledku v původním jazyce
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is an extension of the calculus of variations. It is a mathematical optimization method for deriving control policies. The calculus of variations is concerned with the extrema of functionals. The different approaches tried out in its solution may be considered, in a more or less direct way, as the starting point for new theories. While the true “mathematical” demonstration involves what we now call the calculus of variations, a theory for which Euler and then Lagrange established the foundations, the solution which Johann Bernoulli originally produced, obtained with the help analogy with the law of refraction on optics, was empirical. A similar analogy between optics and mechanics reappears when Hamilton applied the principle of least action in mechanics which Maupertuis justified in the first instance, on the basis of the laws of optics.
Název v anglickém jazyce
En Route for the Calculus of Variations
Popis výsledku anglicky
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is an extension of the calculus of variations. It is a mathematical optimization method for deriving control policies. The calculus of variations is concerned with the extrema of functionals. The different approaches tried out in its solution may be considered, in a more or less direct way, as the starting point for new theories. While the true “mathematical” demonstration involves what we now call the calculus of variations, a theory for which Euler and then Lagrange established the foundations, the solution which Johann Bernoulli originally produced, obtained with the help analogy with the law of refraction on optics, was empirical. A similar analogy between optics and mechanics reappears when Hamilton applied the principle of least action in mechanics which Maupertuis justified in the first instance, on the basis of the laws of optics.
Klasifikace
Druh
J<sub>ost</sub> - Ostatní články v recenzovaných periodicích
CEP obor
—
OECD FORD obor
50200 - Economics and Business
Návaznosti výsledku
Projekt
—
Návaznosti
N - Vyzkumna aktivita podporovana z neverejnych zdroju
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Ratio Mathematica - Journal of Mathematics, Statistics, and Applications
ISSN
1592-7415
e-ISSN
2282-8214
Svazek periodika
36
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
IT - Italská republika
Počet stran výsledku
10
Strana od-do
69 - 78
Kód UT WoS článku
—
EID výsledku v databázi Scopus
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