Some results for an optimal control problem with a semilinear state equation

Fausto Gozzi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 3, page 423-429
  • ISSN: 1120-6330

Abstract

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We consider a quadratic control problem with a semilinear state equation depending on a small parameter ϵ . We show that the optimal control is a regular function of such parameter.

How to cite

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Gozzi, Fausto. "Some results for an optimal control problem with a semilinear state equation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.3 (1988): 423-429. <http://eudml.org/doc/287438>.

@article{Gozzi1988,
abstract = {We consider a quadratic control problem with a semilinear state equation depending on a small parameter $\epsilon$. We show that the optimal control is a regular function of such parameter.},
author = {Gozzi, Fausto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Optimal control; Semilinear state equation; Hamilton-Jacobi equation; quadratic control problem; semilinear state equation},
language = {eng},
month = {9},
number = {3},
pages = {423-429},
publisher = {Accademia Nazionale dei Lincei},
title = {Some results for an optimal control problem with a semilinear state equation},
url = {http://eudml.org/doc/287438},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Gozzi, Fausto
TI - Some results for an optimal control problem with a semilinear state equation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 423
EP - 429
AB - We consider a quadratic control problem with a semilinear state equation depending on a small parameter $\epsilon$. We show that the optimal control is a regular function of such parameter.
LA - eng
KW - Optimal control; Semilinear state equation; Hamilton-Jacobi equation; quadratic control problem; semilinear state equation
UR - http://eudml.org/doc/287438
ER -

References

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  1. BARBU, V. - Hamilton-Jacobi equations and non linear control problems, to appear. Zbl0606.49020
  2. BARBU, V. and DA PRATO, G.- Hamilton-Jacobi equations in Hilbert spaces. Pitman, London (1983). Zbl0508.34001
  3. BARBU, V. and DA PRATO, G. - Hamilton-Jacobi equations in Hilbert spaces; variational and semigroup approach, Annali di Mat. pura ed applicata, (IV), Vol. CXLII, (1985), pp. 303-349. Zbl0508.34001MR839043DOI10.1007/BF01766599
  4. CRANDALL, M.G. and LIONS, P.L. - Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.277, (1983), pp. 1-42. Zbl0599.35024MR690039DOI10.2307/1999343
  5. HENRY, D. - Geometric theory of semilinear parabolic equations, Lecture notes in Math.840, Springer-Verlag, (1981). Zbl0456.35001MR610244
  6. LIONS, J.L. - Optimal control of systems governed by partial differential equations, Springer, Wiesbaden, 1972. Zbl0203.09001
  7. PAZY, A. - Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York-Heidelberg-Berlin, 1983. Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1

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