BibTex RIS Kaynak Göster
Yıl 2014, Cilt: 4 Sayı: 2, 216 - 225, 01.12.2014

Öz

Kaynakça

  • Balachandran, K., and Dauer, J., (2002), Controllability of nonlinear systems in Banach spaces: a survey, Journal of Optimization Theory and Applications, 115, 7–28.
  • Balachandran, K., and Dauer, J., (1998), Local controllability of semilinear evolution systems in
  • Banach spaces, Indian Journal of Pure and Applied Mathematics, 29, 311-320. Bashirov, A. E., (2003), Partially Observable Linear Systems under Dependent Noises; Systems &
  • Control: Foundations & Applications, Birkh¨auser, Basel. Bensoussan, A., (1992), Stochastic Control of Partially Observable Systems, Cambridge University Press, London.
  • Bensoussan, A., Da Prato, G., Delfour, M. C., and Mitter, S. K., (1993), Representation and Control of
  • Infinite Dimensional Systems, Volume 2; Systems & Control: Foundations & Applications, Birkh¨auser, Boston. Bashirov, A. E., Etikan, H., and S¸emi, N., (2010), Partial controllability of stochastic linear systems
  • International Journal of Control, 83, 2564–2572.
  • Bashirov, A. E., Mahmudov, N. I., S¸emi, N., and Etikan, H., (2007), Partial controllability concepts
  • International Journal of Control, 80, 1–7. Bashirov, A. E., and Mahmudov N. I., (1999), On concepts of controllability for deterministic and stochastic systems, SIAM Journal of Control and Optimization, 37, 1808–1821.
  • Bashirov, A. E., and Kerimov, K. R., (1997), On controllability conception for stochastic systems
  • SIAM Journal of Control and Optimization, 35, 384–398. Bashirov, A. E., (1996), On weakening of the controllability concepts, Proceedings of the 35th Con- ference on Decission and Control, Kobe, Japan, December, 1996, 640–645.
  • Bashirov, A. E., and Mahmudov, B. I., (1999), Controllability of linear deterministic and stochas- tic systems, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arisona, USA, December, 1999, 3196–3201.
  • Bashirov, A. E., and Mahmudov, N. I., (1999), Some new results in theory of controllability, Pro- ceedings of the 7th Mediterranean Conference on Control and Automation, Haifa, Israel, June 28–30, , 323–343.
  • Bashirov, A. E., and Jneid, M., (2013), On partial complete controllability of semilinear systems
  • Abstract and Applied Analysis, doi:10.1155/2013/521052, 8 pages.
  • Curtain, R. F., and Zwart, H. J., (1995), An Introduction to Infinite Dimensional Linear Systems
  • Theory, Springer-Verlag, Berlin. Fattorini, H. O., (1967), Some remarks on complete controllability, SIAM Journal of Control, 4, –694.
  • Kalman, R. E., (1960), A new approach to linear Şltering and prediction problems, Transactions of
  • ASME, Series D, Journal of Basic Engineering, 82, 35–45. Klamka, J., (1991), Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.
  • Klamka, J., (2000), Shauder’s Şxed point theorem in nonlinear controllability problems, Control Cy- bernetics, 29, 153–165.
  • Li, X., and Yong, J., (1995), Optimal Control for Infinite Dimensional Systems; Systems & Control
  • Foundations & Applications, Birkh¨auser, Boston. Mahmudov, N. I., (2003), Controllability of semilinear stochastic systems in Hilbert spaces, Journal of Mathematical Analysis and Applications, 288, 197–211.
  • Ren, Y., Hu, L., and Sakthivel, R., (2011), Controllability of impulsive neutral stochastic functional differential inclusions with inŞnite delay, Journal of Computational and Applied Mathematics, 235, –2614.
  • Russel, D. L., (1967), Nonharmonic Fourier series in the control theory of distributed parameter systems, Journal of Mathematical Analysis and Applications, 18, 542–560.
  • Sakthivel, R., Ganesh, R., and Suganya, N., (2012), Approximate controllability of fractional neutral stochastic system with inŞnite delay, Reports on Mathematical Physics, 70, 291–311.
  • Sakthivel, R., Ren, Y., and Mahmudov, N. I., (2011), On approximate controllability of semilinear fractional differential systems, Computers and Mathematics with Applications, 62, 1451–1459.
  • Yan, Z., (2012), Approximate controllability of partial neutral functional differential systems of frac- tional order with state-dependent delay, International Journal of Control, 85, 1051–1062.
  • Zabczyk. J., (1995), Mathematical Control Theory: An Introduction; Systems & Control: Foundations

PARTIAL COMPLETE CONTROLLABILITY OF DETERMINISTIC SEMILINEAR SYSTEMS

Yıl 2014, Cilt: 4 Sayı: 2, 216 - 225, 01.12.2014

Öz

In this paper the concept of partial complete controllability for deterministic semilinear control systems in separable Hilbert spaces is investigated. Some important systems can be expressed as a first order differential equation only by enlarging the state space. Therefore, the ordinary controllability concepts for them are too strong. This motivates the partial controllability concepts, which are directed to the original state space. Based on generalized contraction mapping theorem, a sufficient condition for the partial complete controllability of a semilinear deterministic control system is obtained in this paper. The result is demonstrated through appropriate examples.

Kaynakça

  • Balachandran, K., and Dauer, J., (2002), Controllability of nonlinear systems in Banach spaces: a survey, Journal of Optimization Theory and Applications, 115, 7–28.
  • Balachandran, K., and Dauer, J., (1998), Local controllability of semilinear evolution systems in
  • Banach spaces, Indian Journal of Pure and Applied Mathematics, 29, 311-320. Bashirov, A. E., (2003), Partially Observable Linear Systems under Dependent Noises; Systems &
  • Control: Foundations & Applications, Birkh¨auser, Basel. Bensoussan, A., (1992), Stochastic Control of Partially Observable Systems, Cambridge University Press, London.
  • Bensoussan, A., Da Prato, G., Delfour, M. C., and Mitter, S. K., (1993), Representation and Control of
  • Infinite Dimensional Systems, Volume 2; Systems & Control: Foundations & Applications, Birkh¨auser, Boston. Bashirov, A. E., Etikan, H., and S¸emi, N., (2010), Partial controllability of stochastic linear systems
  • International Journal of Control, 83, 2564–2572.
  • Bashirov, A. E., Mahmudov, N. I., S¸emi, N., and Etikan, H., (2007), Partial controllability concepts
  • International Journal of Control, 80, 1–7. Bashirov, A. E., and Mahmudov N. I., (1999), On concepts of controllability for deterministic and stochastic systems, SIAM Journal of Control and Optimization, 37, 1808–1821.
  • Bashirov, A. E., and Kerimov, K. R., (1997), On controllability conception for stochastic systems
  • SIAM Journal of Control and Optimization, 35, 384–398. Bashirov, A. E., (1996), On weakening of the controllability concepts, Proceedings of the 35th Con- ference on Decission and Control, Kobe, Japan, December, 1996, 640–645.
  • Bashirov, A. E., and Mahmudov, B. I., (1999), Controllability of linear deterministic and stochas- tic systems, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arisona, USA, December, 1999, 3196–3201.
  • Bashirov, A. E., and Mahmudov, N. I., (1999), Some new results in theory of controllability, Pro- ceedings of the 7th Mediterranean Conference on Control and Automation, Haifa, Israel, June 28–30, , 323–343.
  • Bashirov, A. E., and Jneid, M., (2013), On partial complete controllability of semilinear systems
  • Abstract and Applied Analysis, doi:10.1155/2013/521052, 8 pages.
  • Curtain, R. F., and Zwart, H. J., (1995), An Introduction to Infinite Dimensional Linear Systems
  • Theory, Springer-Verlag, Berlin. Fattorini, H. O., (1967), Some remarks on complete controllability, SIAM Journal of Control, 4, –694.
  • Kalman, R. E., (1960), A new approach to linear Şltering and prediction problems, Transactions of
  • ASME, Series D, Journal of Basic Engineering, 82, 35–45. Klamka, J., (1991), Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.
  • Klamka, J., (2000), Shauder’s Şxed point theorem in nonlinear controllability problems, Control Cy- bernetics, 29, 153–165.
  • Li, X., and Yong, J., (1995), Optimal Control for Infinite Dimensional Systems; Systems & Control
  • Foundations & Applications, Birkh¨auser, Boston. Mahmudov, N. I., (2003), Controllability of semilinear stochastic systems in Hilbert spaces, Journal of Mathematical Analysis and Applications, 288, 197–211.
  • Ren, Y., Hu, L., and Sakthivel, R., (2011), Controllability of impulsive neutral stochastic functional differential inclusions with inŞnite delay, Journal of Computational and Applied Mathematics, 235, –2614.
  • Russel, D. L., (1967), Nonharmonic Fourier series in the control theory of distributed parameter systems, Journal of Mathematical Analysis and Applications, 18, 542–560.
  • Sakthivel, R., Ganesh, R., and Suganya, N., (2012), Approximate controllability of fractional neutral stochastic system with inŞnite delay, Reports on Mathematical Physics, 70, 291–311.
  • Sakthivel, R., Ren, Y., and Mahmudov, N. I., (2011), On approximate controllability of semilinear fractional differential systems, Computers and Mathematics with Applications, 62, 1451–1459.
  • Yan, Z., (2012), Approximate controllability of partial neutral functional differential systems of frac- tional order with state-dependent delay, International Journal of Control, 85, 1051–1062.
  • Zabczyk. J., (1995), Mathematical Control Theory: An Introduction; Systems & Control: Foundations
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Agamirza E. Bashirov Bu kişi benim

Maher Jneid Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 4 Sayı: 2

Kaynak Göster