[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Relative Controllability of Nonlinear Neutral Fractional Volterra Integrodifferential Systems with Multiple Delays in Control

Journal of Applied Nonlinear Dynamics 5(2) (2016) 147--160 | DOI:10.5890/JAND.2016.06.002

K. Balachandran; S. Divya

Department of Mathematics, Bharathiar University, Coimbatore-641046, India

Download Full Text PDF

 

Abstract

In this work, we investigate the global relative controllability of nonlinear neutral fractional Volterra integrodifferential systems with multiple delays. Controllability criteria for nonlinear fractional order systems are established. The results are obtained by using the Schauder fixed point theorem. Moreover, some numerical examples are provided to illustrate the effectiveness and applicability of the proposed criteria.

References

  1. [1]  Das, S. (2008), Functional fractional calculus for system identification and controls, Springer: New York.
  2. [2]  Luchko, Y.F., Rivero, M., Trujillo, J.J. and Velasco, M.P. (2010), FractionalModels: non-locality and complex systems, Computers and Mathematics with Applications, 59, 1048-1056.
  3. [3]  Oldham, K.B. and Spanier, J. (1974), The Fractional Calculus, Academic Press: London.
  4. [4]  Podlubny, I. (1998), Fractional Differential Equations, Elsevier Science and Technology: Amsterdam.
  5. [5]  Agrawal, O.P. (2008), A quadratic numerical scheme for fractional optimal control problems, ASME Journal of Dynamic Systems, Measurement, Control, 130, doi:011010.1-011010.6.
  6. [6]  Miller, K.S. and Ross, B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
  7. [7]  Magin, R.L. (2006), Fractional calculus in bioengineering, Begell House Publisher: Connecticut.
  8. [8]  Koeller, R.C. (1990), Application of fractional calculus to the theory of viscoelasticity, Journal of Applied Mechanics, 4, 529-548.
  9. [9]  Oustaloup, A., Leveron, F., Mathieu, B. and Nanot, F.M. (2000), Frequency-band complex non integer differentiator: Characterization and synthesis, IEEE Transactions on Circuits and Systems, 147, 25-39.
  10. [10]  Podlubny, I. (1999), Fractional order systems and PIλDμ -controllers, IEEE Transactions on Automatic Control, 44, 208-214.
  11. [11]  Ichise,M., Nagayanagi, Y. and Kojima, T. (1971), An analog simulation of non-integer order transfer functions for analysis of electrode processes, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry , 33, 253-265.
  12. [12]  Sun, H.H., Abdelwahab, A.A. and Onaral, B. (1984), Linear approximation of transfer function wih a pole of fractional power, IEEE Transactions on Automatic Control, 29, 441-444.
  13. [13]  Machado, J.T., Kiryakova, V. and Mainardi, F. (2010), Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, 16, 1140-1153.
  14. [14]  Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006), Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
  15. [15]  Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993), Fractional Integrals and Derivatives; Theory and Applications, Gordon and Breach, Amsterdam.
  16. [16]  Podlubny, I. (1999), Fractional Differential Equations, Academic Press, New York.
  17. [17]  Burton, T.A. (1983), Volterra Integral and Differential Equations, Academic Press, New York.
  18. [18]  Xu, H. (2009), Analytical approximations for population growth model with fractional order , Communications in Nonlinear Science and Numerical Simulation, 14,1978-1983.
  19. [19]  Artstein, Z. (1982), Linear systems with delayed controls- A reduction, IEEE Transcations on Automatic Control, AC-27, 869-879.
  20. [20]  Manitius, A. (1974), Mathematical models of Hereditary Systems, Research Report CRM-462, Centre dé Researches Mathematiques, Universite dé Montreal, Montreal.
  21. [21]  Balachandran, K. (1987), Global relative controllability of nonlinear systems with time varying multiple delays in control, International Journal of Control, 46, 193-200.
  22. [22]  Balachandran, K. and Somasundaram, D. (1984), Controllability of nonlinear systems consisting of a bilinear mode with time varying delays in control, Automatica, 20, 257-258.
  23. [23]  Balachandran, K. and Somasundaram, D. (1985), Controllability of nonlinear systems with time varying delays in control, Kybernetika, 21, 65-72.
  24. [24]  Dauer, J.P and Gahl, R.D. (1977), Controllability of nonlinear delay systems, Journal of Optimization Theory and Applications, 21, 59-70.
  25. [25]  Klamka, J. (1976), Relative controllability of nonlinear systems with delay in control, Automatica, 12, 633- 634.
  26. [26]  Balachandran, K., Divya, S., Rivero, M. and Trujillo, J.J. (2015), Controllability of nonlinear implicit neutral fractional Volterra integrodifferential systems, Journal of Vibration and control, DOI:10.1177/1077546314567182, (in press).
  27. [27]  Balachandran, K., Zhou, Y. and Kokila, J. (2012), Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation, 17, 3508-3520.
  28. [28]  Balachandran, K. and Govindaraj, V. (2014), Numerical controllability of fractional dynamical systems, Optimization, 63, 1267-1279.
  29. [29]  Balachandran, K. and Divya, S. (2014), Controllability of nonlinear implicit fractional integrodifferential systems, International Journal of Applied Mathematics and Computer Science, 24, 713-722.
  30. [30]  Kexue, L. and Jigen, P. (2011), Laplace transform and fractional differntial equations, Applied Mathematics Letters, 24, 2019-2023.
  31. [31]  Balachandran, K., Kokila, J. and Trujillo, J.J. (2012), Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Applications, 64, 3037-3045.
  32. [32]  Dauer, J.P. (1976), Nonlinear perturbations of quasi-linear control systems, Journal of Mathematical Analysis and Applications, 54, 717-725.
  33. [33]  Do, V.N. (1990), Controllability of semilinear systems, Journal of Optimization Theory and Applications, 65, 41-52.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates