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Optimization of controlled systems with delays considering non-fixed initial moment, mixed initial conditions and restrictions (GNSF/ST06/3-046G)


Funded by

SRNSFGShota Rustaveli National Science Foundation of Georgia

Start Date: 2006-10-01       End Date: 2008-10-01

Proving of the necessary conditions of optimality for non-linear optimal problems with delays and quasi-linear neutral optimal problems in the case of non-fixed initial moment, mixed and functional restrictions. Construction and optimization of mathematical models for economical problems of distribution of investments and with restrictions of “narrow place” type, considering the factor of delay.

Project members:

Talks

  • Optimization of delay control systems with non-fixed initial moment, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at The Fourth International Conference of Applied Mathematics and Computing, 2007, Bulgaria, Plovdiv.
  • Optimization of delay dynamical systems with mixed initial condition, by Tamaz Tadumadze (Speaker), Guram Kharatishvili at Symposium on Contemporary Mathematics and its Applications, 2007, Batumi, Georgia.
  • Title-Optimization of delay variable structure control systems with mixed intermediate condition, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at Symposium on Contemporary Mathematics and its Applications, 2007, Batumi, Georgia.
  • Optimization of delay controlled systems with non-fixed initial moment nd mixed initial condition, by Tamaz Tadumadze (Speaker) at International Conference on Modern Problems in Applied Mathematics, 2008, Tbilisi, Georgia.
  • Formulas of variation of solution for variable structure delay differential equation with mixed intermediate condition and their applications in optimal problems, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at International Conference on Modern Problems in Applied Mathematics, 2008, Tbilisi, Georgia.

Publications

  • Guram Kharatishvili, Tamaz Tadumadze, Optimization of delay dynamical systems with mixed initial condition, Bull. Georg. Nati. Acad. Sci., v.1, no. 4 , 20-26, Georgian Academy Press, 2007.
  • Tamaz Tadumadze, Akaki Arsenashvili, Optimization of a delay variable structure control system with mixed intermediate condition, Bull. Georg. Nati. Acad. Sci. v.2 , no. 3 , 22-26, Georgian Academy Press, 2008.
  • Tamaz Tadumadze, Optimization of delay controlled systems with non-fixed initial moment and mixed initial condition, Proc. I. Vekua Institute of Applied Mathematics, v. 58, 92-96, TSU, 2008.
  • Tamaz Tadumadze, Formulas of variation for solutions of some classes of functional differential equations and their applications, Formulas of variation for solutions of some classes of functional differential equations and their applications, Elsevier, 2009.
  • Guram Kharatishvili, Tamaz Tadumadze, Optimal control problems with delays and mixed initial condition, J. Math. Sci. (N.Y), vol. 160, No. 2, 221- 245, Springer, 2009.
  • Tamaz Tadumadze, Akaki Arsenashvili, Optimal control of variable structure systems with delays and mixed intermediate condition, Functional Differential Equations. V. 17, No 3-4, 295-317, Ariel University Center of Samaria, 2010.

Additional Information

In the framework of the project articles and abstracts are published in the scientific journals and in the proceedings of international conferences, including:
8.1. Kharatishvili G. and Tadumadze T. Optimization of delay dynamical systems with mixed initial condition, Bull. Georg. Nati. Acad. Sci., v. 1, no.4 (2007), 20-26 .

8.2. Tadumadze T. and Arsenashvili A. Optimization of a delay variable structure control system with mixed intermediate condition, Bull. Georg. Nati. Acad. Sci. v.2, no. 3, 2008.

8.3. Tsintsadze Z. Optimal processes in smooth-convex minimization problems. J. Math.Sci. (N.Y.), v. 148, no. 3, 2008, 399-480.
8.4. Kharatishvili G., Tadumadze T. Optimal control problems with delays and mixed initial condition. J. Math. Sci. (N.Y), vol. 160, No. 2, 2009, 221-245.
8.5. Tadumadze T. Formulas of variation for solutions of some classes of functional differential equations and their applications. Nonlinear Analysis 71 (2009) 706-710 .
8.6. Alkhazishvili L. and Iordanishvili M. Local variation formulas for solution of delay control differential equation with mixed initial condition. Memoirs on Differential Equations and Mathematical Physics 51, 2010, 17–41.
8.7. Tadumadze T. and Arsenashvili A. Optimization of delay control systems with non-fixed initial condition. Fourth International Conference of Applied Mathematics and Computing, Plovdiv, Bulgaria, August 12-18, 2007, v.4, N-Z, 519 p.

8.8. Gorgodze N., Ramishvili I. Formulas of variation for a solution of neutral differential equation with mixed initial condition, Symposium on ,, Contemporary Mathematics and its Applications”, Batumi, Georgia, September 17- 21, 2007, 17 p .

8.9. Alkhazishvili L. , Iordanishvili M. Formulas of variation of solution for delay controlled differential equation with mixed iniial condition and their applications in optimal problems with incommensurable delays I controls, International Conference on Modern Problems in Applied Mathematics, 7-9 October,2008, Tbilisi, 44 p.

8.10. Tsintsadze Z. The extremal principle in quasilinear control systems of neutral type, International Conference on Modern Problems in Applied Mathematics, 7-9 October,2008, Tbilisi, 48 p.