About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 521052, 8 pages
http://dx.doi.org/10.1155/2013/521052
Research Article

On Partial Complete Controllability of Semilinear Systems

Eastern Mediterranean University, Gazimagusa, North Cyprus, P.O. Box 95, Mersin 10, Turkey

Received 27 March 2013; Revised 28 May 2013; Accepted 11 June 2013

Academic Editor: Sakthivel Rathinasamy

Copyright © 2013 Agamirza E. Bashirov and Maher Jneid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Basic Engineering D, Transactions of ASME, vol. 82, pp. 35–45, 1960.
  2. H. O. Fattorini, “Some remarks on complete controllability,” SIAM Journal on Control, vol. 4, pp. 686–694, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. L. Russell, “Nonharmonic Fourier series in the control theory of distributed parameter systems,” Journal of Mathematical Analysis and Applications, vol. 18, pp. 542–560, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory, Springer, Berlin, Germany, 1995.
  5. A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, UK, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. Bensoussan, G. Da Prato, M. C. Delfour, and S. K. Mitter, Representation and Control of Infinite Dimensional Systems, Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 2nd edition, 2007. View at MathSciNet
  7. J. Zabczyk, Mathematical Control Theory: An Introduction, Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 1995. View at MathSciNet
  8. A. E. Bashirov, Partially Observable Linear Systems under Dependent Noises, Systems & Control: Foundations & Applications, Birkhäuser, Basel, Switzerland, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Klamka, Controllability of Dynamical Systems, vol. 48 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991. View at MathSciNet
  10. K. Balachandran and J. P. Dauer, “Controllability of nonlinear systems in Banach spaces: a survey,” Journal of Optimization Theory and Applications, vol. 115, no. 1, pp. 7–28, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  11. K. Balachandran and J. P. Dauer, “Local controllability of semilinear evolution systems in Banach spaces,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 3, pp. 311–320, 1998. View at Zentralblatt MATH · View at MathSciNet
  12. J. Klamka, “Schauder's fixed-point theorem in nonlinear controllability problems,” Control and Cybernetics, vol. 29, no. 1, pp. 153–165, 2000. View at Zentralblatt MATH · View at MathSciNet
  13. N. I. Mahmudov, “Controllability of semilinear stochastic systems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 197–211, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X. J. Li and J. M. Yong, Optimal Control Theory for Infinite-Dimensional Systems, Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  15. R. Sakthivel, N. I. Mahmudov, and J. J. Nieto, “Controllability for a class of fractional-order neutral evolution control systems,” Applied Mathematics and Computation, vol. 218, no. 20, pp. 10334–10340, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Sakthivel, R. Ganesh, and S. Suganya, “Approximate controllability of fractional neutral stochastic system with infinite delay,” Reports on Mathematical Physics, vol. 70, no. 3, pp. 291–311, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. Sakthivel, Y. Ren, and N. I. Mahmudov, “On the approximate controllability of semilinear fractional differential systems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1451–1459, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Yan, “Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay,” International Journal of Control, vol. 85, no. 8, pp. 1051–1062, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Y. Ren, L. Hu, and R. Sakthivel, “Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2603–2614, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A. E. Bashirov, H. Etikan, and N. Şemi, “Partial controllability of stochastic linear systems,” International Journal of Control, vol. 83, no. 12, pp. 2564–2572, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. E. Bashirov, N. Mahmudov, N. Şemi, and H. Etikan, “Partial controllability concepts,” International Journal of Control, vol. 80, no. 1, pp. 1–7, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. A. E. Bashirov and N. I. Mahmudov, “On concepts of controllability for deterministic and stochastic systems,” SIAM Journal on Control and Optimization, vol. 37, no. 6, pp. 1808–1821, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. A. E. Bashirov and K. R. Kerimov, “On controllability conception for stochastic systems,” SIAM Journal on Control and Optimization, vol. 35, no. 2, pp. 384–398, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. E. Bashirov, “On weakening of the controllability concepts,” in Proceedings of the 35th Conference on Decission and Control, pp. 640–645, Kobe, Japan, 1996.
  25. A. E. Bashirov and N. I. Mahmudov, “Controllability of linear deterministic and stochastic systems,” in Proceedings of the 38th Conference on Decission and Control, pp. 3196–3201, Phoenix, Aris, USA, 1999.
  26. A. E. Bashirov and N. I. Mahmudov, “Some new results in theory of controllability,” in Proceedings of the 7th Mediterranean Conference on Control and Automation, pp. 323–343, Haifa, Israel, 1999.
  27. L. Byszewski, “Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem,” Journal of Mathematical Analysis and Applications, vol. 162, no. 2, pp. 494–505, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet