On the existence of optimal controls for nonlinear infinite dimensional systems

Antonella Fiacca; Nikolaos S. Papageorgiou; Francesca Papalini

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 2, page 291-312
  • ISSN: 0011-4642

Abstract

top
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.

How to cite

top

Fiacca, Antonella, Papageorgiou, Nikolaos S., and Papalini, Francesca. "On the existence of optimal controls for nonlinear infinite dimensional systems." Czechoslovak Mathematical Journal 48.2 (1998): 291-312. <http://eudml.org/doc/30419>.

@article{Fiacca1998,
abstract = {We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.},
author = {Fiacca, Antonella, Papageorgiou, Nikolaos S., Papalini, Francesca},
journal = {Czechoslovak Mathematical Journal},
keywords = {evolution triple; optimal control; monotone operator; hemicontinuous operator; parabolic system; property $(Q)$; evolution triple; optimal control; monotone operator; hemicontinuous operator; parabolic system; property },
language = {eng},
number = {2},
pages = {291-312},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of optimal controls for nonlinear infinite dimensional systems},
url = {http://eudml.org/doc/30419},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Fiacca, Antonella
AU - Papageorgiou, Nikolaos S.
AU - Papalini, Francesca
TI - On the existence of optimal controls for nonlinear infinite dimensional systems
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 291
EP - 312
AB - We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
LA - eng
KW - evolution triple; optimal control; monotone operator; hemicontinuous operator; parabolic system; property $(Q)$; evolution triple; optimal control; monotone operator; hemicontinuous operator; parabolic system; property
UR - http://eudml.org/doc/30419
ER -

References

top
  1. Optimal Control of Distributed Parameter Systems, North Holland, New York, 1981. (1981) MR0624064
  2. 10.1016/0362-546X(87)90092-7, Nonlinear Analysis 11 (1987), 1399–1404. (1987) MR0917861DOI10.1016/0362-546X(87)90092-7
  3. Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. (1976) Zbl0328.47035MR0390843
  4. Optimal Control Theory, Springer-Verlag, New York, 1974. (1974) Zbl0295.49001MR0372707
  5. 10.1090/S0002-9947-1966-0203542-1, Trans. Amer. Math. Society 124 (1966), 369–412. (1966) Zbl0145.12501MR0203542DOI10.1090/S0002-9947-1966-0203542-1
  6. Optimization-Theory and Applications, Springer-Verlag, New York, 1983. (1983) Zbl0506.49001MR0688142
  7. 10.1512/iumj.1979.28.28039, Indiana J. Math. 28 (1979), 559–579. (1979) Zbl0418.46034MR0542944DOI10.1512/iumj.1979.28.28039
  8. 10.4064/sm-78-2-213-215, Studia Math. 78 (1983), 213–215. (1983) MR0766717DOI10.4064/sm-78-2-213-215
  9. 10.2140/pjm.1982.103.39, Pacific Journal Math. 103 (1982), 39–56. (1982) MR0687963DOI10.2140/pjm.1982.103.39
  10. 10.1007/BF01875294, Siberian Math. J. 19 (1979), 434–438. (1979) Zbl0409.54048DOI10.1007/BF01875294
  11. Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin, 1971. (1971) Zbl0203.09001MR0271512
  12. On measurable multifunctions with applications to random multivalued equations, Math. Japonica 32 (1987), 437–464. (1987) Zbl0634.28005MR0914749
  13. 10.1155/S0161171287000516, Intern. J. Math. and Math. Sci. 10 (1987), 433–442. (1987) Zbl0619.28009MR0896595DOI10.1155/S0161171287000516
  14. 10.1137/0315056, SIAM J. Control Optim. 15 (1977), 859–903. (1977) MR0486391DOI10.1137/0315056
  15. Nonlinear Functional Analysis and Its Application II, Springer, New York, 1990. (1990) MR0816732

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.