Time-optimal boundary control of a parabolic system with time lags given in integral form

Adam Kowalewski; Anna Krakowiak

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 3, page 287-295
  • ISSN: 1641-876X

Abstract

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In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.

How to cite

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Kowalewski, Adam, and Krakowiak, Anna. "Time-optimal boundary control of a parabolic system with time lags given in integral form." International Journal of Applied Mathematics and Computer Science 16.3 (2006): 287-295. <http://eudml.org/doc/207793>.

@article{Kowalewski2006,
abstract = {In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.},
author = {Kowalewski, Adam, Krakowiak, Anna},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {parabolic system; time lags; time-optimal boundary control},
language = {eng},
number = {3},
pages = {287-295},
title = {Time-optimal boundary control of a parabolic system with time lags given in integral form},
url = {http://eudml.org/doc/207793},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Kowalewski, Adam
AU - Krakowiak, Anna
TI - Time-optimal boundary control of a parabolic system with time lags given in integral form
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 3
SP - 287
EP - 295
AB - In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.
LA - eng
KW - parabolic system; time lags; time-optimal boundary control
UR - http://eudml.org/doc/207793
ER -

References

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  3. Knowles G. (1978): Time optimal control of parabolic systems with boundary conditions involving time delays. - J. Optim. Theory Applics., Vol. 25, No. 4, pp. 563-574. Zbl0368.49007
  4. Kowalewski A. (1988): Boundary control of distributed parabolic system with boundary condition involving a time-varying lag. -Int. J. Contr., Vol. 48, No. 6, pp. 2233-2248. Zbl0662.49011
  5. Kowalewski A. (1990a): Feedback control for a distributed parabolic system with boundary condition involving a time-varying lag. - IMA J. Math. Contr. Inf., Vol. 7, No. 2, pp. 143-157. Zbl0717.49018
  6. Kowalewski A. (1990b): Optimal control of distributed parabolic systems involving time lags. - IMA J. Math. Contr. Inf., Vol. 7, No. 4, pp. 375-393. Zbl0721.49022
  7. Kowalewski A. (1993): Optimal control of parabolic systems with time-varying lags. - IMA J. Math. Contr. Inf., Vol. 10,No. 2, pp. 113-129. Zbl0874.49021
  8. Kowalewski A. (1998): Optimal control of distributed parabolic systems with multiple time-varying lags. - Int. J. Contr., Vol. 69, No. 3, pp. 361-381. Zbl0942.49005
  9. Kowalewski A. (1999): Optimization of parabolic systems with deviating arguments.- Int. J. Contr., Vol. 72, No. 11, pp. 947-959. Zbl0980.49005
  10. Kowalewski A. (2001): Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays. - Cracow: University of Mining and Metallurgy Press. 
  11. Kowalewski A. and Duda J. (1992): On some optimal control problemfor a parabolic system with boundary condition involving a time-varying lag.- IMA J. Math. Contr. Inf., Vol. 9, No. 2, pp. 131-146. Zbl0767.49002
  12. Kowalewski A. and Krakowiak A.(2000): Time-optimal control of a parabolic system with time lags given in the integral form. - IMA J. Math. Contr. Inf., Vol. 17, No. 3, pp. 209-225. Zbl0980.49004
  13. Lions J.L. (1971): Optimal Control Systems Governed by Partial Differential Equations. - Berlin: Springer. Zbl0203.09001
  14. Lions J.L. and Magenes E. (1972): Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2. - Berlin: Springer. Zbl0223.35039
  15. Wang P.K.C. (1975): Optimal control of parabolic systems with boundary conditions involving time delays. - SIAM J. Contr.,Vol. 13, No. 2, pp. 274-293. Zbl0301.49009

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