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ON TRACKING OF SOLUTIONS OF PARABOLIC VARIATIONAL INEQUALITIES

Year 2012, Volume 2, Issue 2, 185 - 194, 01.12.2012

Abstract

The problem of constructing a feedback control algorithm for a parabolic variational inequality is considered. This algorithm should provide tracking a prescribed trajectory by a solution of the given inequality. Two solving algorithms, which are stable with respect to informational noises, are designed. The algorithms are based on the method of extremal shift, which is known in the theory of guaranteed control.

References

  • Barbu, V., (1976), Nonlinear Semigroup and Differential Equation in Banach Space, Noordhoof.
  • Barbu, V., (1984), Optimal Control of Variational Inequalities, Pitman.
  • Glovinskii, R., Lions, J.-L. and Tremol’er, R., (1979), Numerical Research of Variational Inequalities, North-Holland, Amsterdam.
  • Krasovskii, N. N. and Subbotin, A.I., (1988), Game-Theoretical Control Problems, Springer Verlag, New York—Berlin.
  • Maksimov, V. I., (1998), Some stable algorithm for solving problems of feedback control and recon- struction for distributed parameter systems, Recent Advances in Numerical Methods and Applications, World ScientiŞc, 757–764.
  • Maksimov, V. I., (2000), Feedback minimax control for parabolic variational inequlity, C.R. Acad. Sci. Paris, t.328, serie IIb, 105–108.
  • Osipov, Yu. S. and Kryazhimskii, A. V., (1995), Inverse Problems for Ordinary Differential Equations: Dynamical Solutions. Gordon and Breach, London.
  • Maksimov, V. I., (2002), Dynamical Inverse Problems of Distributed Systems, VSP, Utrecht—Boston.
  • Samarskii, A.A., (1971), Introduction to the Theory of Difference Schemes, Nauka, Moscow (in Rus- sian).

Year 2012, Volume 2, Issue 2, 185 - 194, 01.12.2012

Abstract

References

  • Barbu, V., (1976), Nonlinear Semigroup and Differential Equation in Banach Space, Noordhoof.
  • Barbu, V., (1984), Optimal Control of Variational Inequalities, Pitman.
  • Glovinskii, R., Lions, J.-L. and Tremol’er, R., (1979), Numerical Research of Variational Inequalities, North-Holland, Amsterdam.
  • Krasovskii, N. N. and Subbotin, A.I., (1988), Game-Theoretical Control Problems, Springer Verlag, New York—Berlin.
  • Maksimov, V. I., (1998), Some stable algorithm for solving problems of feedback control and recon- struction for distributed parameter systems, Recent Advances in Numerical Methods and Applications, World ScientiŞc, 757–764.
  • Maksimov, V. I., (2000), Feedback minimax control for parabolic variational inequlity, C.R. Acad. Sci. Paris, t.328, serie IIb, 105–108.
  • Osipov, Yu. S. and Kryazhimskii, A. V., (1995), Inverse Problems for Ordinary Differential Equations: Dynamical Solutions. Gordon and Breach, London.
  • Maksimov, V. I., (2002), Dynamical Inverse Problems of Distributed Systems, VSP, Utrecht—Boston.
  • Samarskii, A.A., (1971), Introduction to the Theory of Difference Schemes, Nauka, Moscow (in Rus- sian).

Details

Primary Language English
Journal Section Research Article
Authors

Haydar AKCA This is me
Abu Dhabi University, College of Arts and Sciences, Department of Applied Sciences and Mathematics, Abu Dhabi, UAE


Vyacheslav I. MAKSİMOV This is me
Ural Federal University, Graduate School of Economics and Management, and Institute of Mathematics and Mechanics, Ekaterinburg, Russia

Publication Date December 1, 2012
Published in Issue Year 2012, Volume 2, Issue 2

Cite

Bibtex @ { twmsjaem761710, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2012}, volume = {2}, number = {2}, pages = {185 - 194}, title = {ON TRACKING OF SOLUTIONS OF PARABOLIC VARIATIONAL INEQUALITIES}, key = {cite}, author = {Akca, Haydar and Maksimov, Vyacheslav I.} }