Optimal control for n × n coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables

Hussain A. El-Saify; G. M. Bahaa

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 3, page 291-311
  • ISSN: 0232-0525

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El-Saify, Hussain A., and Bahaa, G. M.. "Optimal control for $n\times n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables." Mathematica Slovaca 53.3 (2003): 291-311. <http://eudml.org/doc/34578>.

@article{El2003,
author = {El-Saify, Hussain A., Bahaa, G. M.},
journal = {Mathematica Slovaca},
keywords = {optimal control problem; Dirichlet and Neumann conditions; operator with an infinite number of variables},
language = {eng},
number = {3},
pages = {291-311},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Optimal control for $n\times n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables},
url = {http://eudml.org/doc/34578},
volume = {53},
year = {2003},
}

TY - JOUR
AU - El-Saify, Hussain A.
AU - Bahaa, G. M.
TI - Optimal control for $n\times n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 3
SP - 291
EP - 311
LA - eng
KW - optimal control problem; Dirichlet and Neumann conditions; operator with an infinite number of variables
UR - http://eudml.org/doc/34578
ER -

References

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  1. BAHAA G. M., Quadratic Pareto optimal control of parabolic equation with state-control constraints and an infinite number of variables, IMA J. Math. Control Infoгm. 20 (2003), 167-178. Zbl1029.49023MR1987533
  2. BEREZANSKII, JU. M., Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables, Transl. Math. Monographs 63, Amer. Math. Soc, Providence, RI, 1986. (1986) 
  3. BEREZANSKII, JU. M., Self-adjointness of elliptic operator with an infinite number of variables, Ukrain. Mat. Zh. 27 (1975), 729-742. (1975) MR0405094
  4. EL-SAIFY H. A., Boundary control for the hyperbolic operator with an infinite number of variables, J. Inst. Math. Comput. Sci. Comput. Sci. Ser. 1 (1990), 47-51. (1990) 
  5. EL-SAIFY H. A., Boundary control problem with an infinite number of variables, Internal J. Math. Math. Sci. 28 (2001), 57-62. Zbl0999.49003MR1882683
  6. EL-SAIFY H. A.-BAHAA G. M., Optimal control for nxn systems of hyperbolic types, Rev. Mat. Apl. 22 (2001), 41-58. MR1890942
  7. EL-SAIFY H. A.-SERAG H. M.-BAHAA G. M., On optimal control for nxn elliptic system involving operators with an infinite number of variables, A.M.S.E. Advances in Modeling & Analysis 1-A 37 (2000), 47-61. 
  8. GALI I. M.-EL-SAIFY H. A., Optimal control of a system governed by hyperbolic operator with an infinite number of variables, J. Math. Anal. Appl. 85 (1982), 24-30. (1982) Zbl0563.49013MR0647556
  9. GALI I. M.-EL-SAIFY H. A., Distributed control of a system governed by Dirichlet and Neumann Problems for a self-adjoint elliptic operator with an infinite number of variables, J. Optim. Theory Appl. 39 (1983), 293-298. (1983) Zbl0481.49015MR0693688
  10. IMANUVILOV O. YU., On exact controllability for the Navier-Stokes equations, ESAIM: Control. Optim. Calc. Var. 3 (1998), 97-131. (1998) Zbl1052.93502MR1617825
  11. KOTARSKI W., Optimal control of a system governed by Petrowsky type equation with an infinite number of variables, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 35 (1996), 73-82. (1996) Zbl0961.49011MR1485046
  12. KOTARSKI W.-EL-SAIFY H. A.-BAHAA G. M., Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay, IMA J. Math. Control Inform. 19 (2002), 461-476. Zbl1044.49018MR1949014
  13. KOTARSKI W.-EL-SAIFY H. A.-BAHAA G. M., Optimal control problem for a hyperbolic system with mixed control-state constraints involving operator of infinite order, Internat. J. Pure Appl. Math. 1 (2002), 241-254. Zbl1009.49021MR1912680
  14. LI X.-YONG J., Optimal Control Theory for Infinite Dimensional Systems, Birkhauser, Boston, 1995. (1995) MR1312364
  15. LIONS J. L., Optimal Control of Systems Governed by Partial Differential Equations, Grundlehren Math. Wiss. 170, Springer-Verlag, Berlin-Heidelberg-New York, 1971. (1971) Zbl0203.09001MR0271512
  16. LIONS J. L.-ENRIQUE Z., Approximate controllability of a hydro-elastic coupled system, ESAIM: Control. Optim. Calc. Var. 1 (1995), 1-15. (1995) Zbl0878.93034MR1382513
  17. LIONS J. L.-MAGENES E., Non-Homogeneous Boundary Value Problem and Applications, Vol. I. Grundlehren Math. Wiss. 181, Springer-Verlag, Berlin-Heidelberg-New York, 1972. (1972) MR0350177

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