About: Riccati Equations and their Solution

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Description	A Riccati equation, deriving its name from Jacopo Francesco, Count Riccati (1676–1754) [1], who studied a particular case of this equation from 1719 to 1724. For several reasons, a differential equation of the form of Equation 14.1, and generalizations thereof comprise a highly significant class of nonlinear ordinary differential equations. First, they are intimately related to ordinary linear homogeneous differential equations of the second order. Second, the solutions of Equation 14.1 possess a very particular structure in that the general solution is a fractional linear function in the constant of integration. In applications, Riccati differential equations appear in the classical problems of the calculus of variations and in the associated disciplines of optimal control and filtering A Riccati equation, deriving its name from Jacopo Francesco, Count Riccati (1676–1754) [1], who studied a particular case of this equation from 1719 to 1724. For several reasons, a differential equation of the form of Equation 14.1, and generalizations thereof comprise a highly significant class of nonlinear ordinary differential equations. First, they are intimately related to ordinary linear homogeneous differential equations of the second order. Second, the solutions of Equation 14.1 possess a very particular structure in that the general solution is a fractional linear function in the constant of integration. In applications, Riccati differential equations appear in the classical problems of the calculus of variations and in the associated disciplines of optimal control and filtering (en)
Title	Riccati Equations and their Solution Riccati Equations and their Solution (en)
skos:prefLabel	Riccati Equations and their Solution Riccati Equations and their Solution (en)
skos:notation	RIV/67985556:_____/11:00436431!RIV15-AV0-67985556
http://linked.open...avai/riv/aktivita	I P Z
http://linked.open...avai/riv/aktivity	I, P(1M0567), Z(AV0Z10750506)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Kučera, Vladimír
http://linked.open.../riv/druhVysledku	C - Kapitola v knize
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	227034
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/11:00436431
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Riccati equation; optimal control; solution (en)
http://linked.open.../riv/klicoveSlovo	Riccati equation optimal control solution
http://linked.open...ontrolniKodProRIV	[AABF24BCB724]
http://linked.open...i/riv/mistoVydani	Boca Raton
http://linked.open...vEdiceCisloSvazku	Electrical Engineering Handbook
http://linked.open...i/riv/nazevZdroje	The Control Handbook, Second Edition: Control System Advanced Methods
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...v/pocetStranKnihy	3526 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Centre for Applied Cybernetics
http://linked.open...UplatneniVysledku	2011
http://linked.open...iv/tvurceVysledku	Kučera, Vladimír
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
number of pages	23 (xsd:int)
http://purl.org/ne...btex#hasPublisher	CRC Press
https://schema.org/isbn	978-1-4200-7366-9

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