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  • An alternative proof of solvability of the differential equation that is a part of the Regulator Equation which arises from the solution of the Output Regulation Problem is presented. The proof uses the standard Hilbert-space based theory of solutions of elliptic partial differential equations for the case of the linear Output Regulation Problem. In the nonlinear case, a sequence of linear equations is defined so that their solution converges to the solution of the nonlinear problem. This is proved using the Banach Contraction Theorem.
  • An alternative proof of solvability of the differential equation that is a part of the Regulator Equation which arises from the solution of the Output Regulation Problem is presented. The proof uses the standard Hilbert-space based theory of solutions of elliptic partial differential equations for the case of the linear Output Regulation Problem. In the nonlinear case, a sequence of linear equations is defined so that their solution converges to the solution of the nonlinear problem. This is proved using the Banach Contraction Theorem. (en)
  • V článku je prezentován alternativní důkaz řešitelnosti diferenciální rovnice, která je součástí rovnice regulátoru. Pro důkaz řešitelnosti rivnice regulátoru vznikající při řešení lineárního problému regulace výstupu se používá standardní teorie řešitelnosti eliptických parciálních diferenciálních rovnic založená na Hilbertových prostorech. V nelineárním případě se konstruuje posloupnost lineárních problémů, jejichž řešení konvergují k řešení nelineárního problému, což je dokazováno pomocí Banachovy věty o pevném bodě. (cs)
Title
  • Solvability of the Regulator Equation: L2-space Approach
  • Solvability of the Regulator Equation: L2-space Approach (en)
  • Řešitelnost rovnice regulátoru v L2 prostorech (cs)
skos:prefLabel
  • Solvability of the Regulator Equation: L2-space Approach
  • Solvability of the Regulator Equation: L2-space Approach (en)
  • Řešitelnost rovnice regulátoru v L2 prostorech (cs)
skos:notation
  • RIV/67985556:_____/08:00310750!RIV09-GA0-67985556
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GP102/07/P413), P(LA 274), Z(AV0Z10750506)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 395842
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  • RIV/67985556:_____/08:00310750
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  • Output Regulation Problem; Nonlinear Systems; Partial Differential Equations (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [9BCAA98B8262]
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  • Seoul
http://linked.open...i/riv/mistoVydani
  • Laxenburg
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  • Preprints of the 17th IFAC World Congress
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http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Rehák, Branislav
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
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  • IFAC
https://schema.org/isbn
  • 978-3-902661-00-5
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