The Origination of the Calculus of Variations

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The Origination of the Calculus of Variations

Popis výsledku v původním jazyce

This article considers something about the origin of the calculus of variations. 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 a set of differential equations describing the paths of the control variables that minimize the cost functional. Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The calculus of variations is concerned with the maxima or minima of functionals, which are collectively called extrema. Indeed, 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

Název v anglickém jazyce

The Origination of the Calculus of Variations

Popis výsledku anglicky

This article considers something about the origin of the calculus of variations. 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 a set of differential equations describing the paths of the control variables that minimize the cost functional. Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The calculus of variations is concerned with the maxima or minima of functionals, which are collectively called extrema. Indeed, 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

Druh

O - Ostatní výsledky

CEP obor

AB - Dějiny

OECD FORD obor

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Projekt

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Návaznosti

N - Vyzkumna aktivita podporovana z neverejnych zdroju

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů