[ 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

Complete Controllability of Nonlinear Neural Network Control Systems

Journal of Applied Nonlinear Dynamics 13(3) (2024) 583--590 | DOI:10.5890/JAND.2024.09.013

Amarnath Chaurasia, Santosh Kumar Tripathi, Anurag Shukla, Swati Maurya

Rajkiya Engineering College, Kannauj, Uttar Pradesh-209732, India

Download Full Text PDF

 

Abstract

In this paper complete controllability of nonlinear neural control network systems is discussed. Using suitable substitution assumed system is converted in the first-order nonlinear differential equation with a nonzero linear part. With the use of controllability Grammian matrix, Lipschitz type nonlinearity, and fixed point theorem, some sufficient conditions for the complete controllability are derived. In the end, one numerical example and one LR (inductance and resistance) circuit example are discussed to validate the theoretical results.

References

  1. [1]  Mahmudov, N.I., Vijayakumar, V., and Murugesu, R. (2016), Approximate controllability of second-order evolution differential inclusions in Hilbert spaces, Mediterranean Journal of Mathematics, 13, 3433-3454.
  2. [2]  Vijayakumar, V., Panda, S.K., Nisar, K.S., and Baskonus, H.M. (2021), Results on approximate controllability results for second order Sobolev type impulsive neutral differential evolution inclusions with infinite delay, Numerical Methods for Partial Differential Equations, 37(2), 1200-1221.
  3. [3]  Vijayakumar, V. (2018), Approximate controllability results for abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces, IMA Journal of Mathematical Control and Information, 35(1), 297-314.
  4. [4]  Vijayakumar, V. (2018), Approximate controllability results for analytic resolvent integro-differential inclusions in Hilbert spaces, International Journal of Control, 91(1), 204-214.
  5. [5]  Vijayakumar, V., Udhayakumar, R., and Dineshkumar, C. (2021), Approximate controllability of second order nonlocal neutral differential evolution inclusions, IMA Journal of Mathematical Control and Information, 38(1), 192-210.
  6. [6]  Vijayakumar, V. and Murugesu, R. (2019), Controllability for a class of second-order evolution differential inclusions without compactness, Applicable Analysis, 98(7), 1367-1385.
  7. [7]  Vijayakumar, V., Murugesu, R., Poongodi, R., and Dhanalakshmi, S. (2017), Controllability of second-order impulsive nonlocal Cauchy problem via measure of noncompactness, Mediterranean Journal of Mathematics, 14, 1-23.
  8. [8]  Vijayakumar, V. (2018), Approximate controllability for a class of second-order stochastic evolution inclusions of Clarke's subdifferential type, Results in Mathematics, 73(1), 42.
  9. [9]  Sivasankaran, S., Arjunan, M.M., and Vijayakumar, V. (2011), Existence of global solutions for second order impulsive abstract partial differential equations, Nonlinear Analysis: Theory, Methods $\&$ Applications, 74(17), 6747-6757.
  10. [10]  Sakthivel, R. and Ren, Y. (2011), Complete controllability of stochastic evolution equations with jumps, Reports on Mathematical Physics, 68(2), 163-174.
  11. [11]  Mohan Raja, M., Vijayakumar, V., Shukla, A., Nisar, K.S., and Rezapour, S. (2021), New discussion on nonlocal controllability for fractional evolution system of order $1< r< 2$, Advances in Difference Equations, 2021(1), 1-19.
  12. [12]  Vijayakumar, V., Nisar, K.S., Chalishajar, D., Shukla, A., Malik, M., Alsaadi, A., and Aldosary, S.F. (2022), A note on approximate controllability of fractional semilinear integrodifferential control systems via resolvent operators, Fractal and Fractional, 6(2), 73.
  13. [13]  Gautam, P., Shukla, A., and Patel, R. (2022), Results on impulsive semilinear differential equations with control functions, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.8363.
  14. [14]  Klamka, J. (2009), Stochastic controllability of systems with multiple delays in control, International Journal of Applied Mathematics and Computer Science, 19(1), 39.
  15. [15]  Kavitha, K., Nisar, K.S., Shukla, A., Vijayakumar, V., and Rezapour, S. (2021), A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems, Advances in Difference Equations, 2021(1), 1-18.
  16. [16]  Shukla, A., Sukavanam, N., and Pandey, D.N. (2014), Controllability of semilinear stochastic system with multiple delays in control, IFAC Proceedings Volumes, 47(1), 306-312.
  17. [17]  Dos Santos, J.P.C., Vijayakumar, V., and Murugesu, R. (2013), Existence of mild solutions for nonlocal Cauchy problem for fractional neutral integro-differential equation with unbounded delay, Communications in Mathematical Analysis, 14(1), 59-71.
  18. [18]  Raja, M.M., Vijayakumar, V., and Udhayakumar, R. (2020), A new approach on approximate controllability of fractional evolution inclusions of order $1< r< 2$ with infinite delay, Chaos, Solitons $\&$ Fractals, 141, p.110343.
  19. [19]  Zhou, Y., Vijayakumar, V., Ravichandran, C., and Murugesu, R. (2017), Controllability results for fractional order neutral functional differential inclusions with infinite delay, Fixed Point Theory, 18(2), 773-798.
  20. [20]  Kavitha Williams, W., Vijayakumar, V., Udhayakumar, R., Panda, S.K., and Nisar, K.S. (2020), Existence and controllability of nonlocal mixed Volterra-Fredholm type fractional delay integro-differential equations of order $1< r< 2$, Numerical Methods for Partial Differential Equations, 1-19.
  21. [21]  Vijayakumar, V. and Udhayakumar, R. (2021), A new exploration on existence of Sobolev-type Hilfer fractional neutral integro-differential equations with infinite delay, Numerical Methods for Partial Differential Equations, 37(1), 750-766.
  22. [22]  Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Shukla, A., and Nisar, K.S. (2021), A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order $r\in (1, 2)$ with delay, Chaos, Solitons $\&$ Fractals, 153, p.111565.
  23. [23]  Vijayakumar, V., Ravichandran, C., Nisar, K.S., and Kucche, K.D. (2021), New discussion on approximate controllability results for fractional Sobolev type Volterra-Fredholm integro-differential systems of order $1< r< 2$, Numerical Methods for Partial Differential Equations, 1-20.
  24. [24]  Dineshkumar, C., Sooppy Nisar, K., Udhayakumar, R., and Vijayakumar, V. (2022), A discussion on approximate controllability of Sobolev-type Hilfer neutral fractional stochastic differential inclusions, Asian Journal of Control, 24(5), 2378-2394.
  25. [25]  Liu, Y.Y., Slotine, J.J., and Barabasi, A.L. (2011), Controllability of complex networks, Nature, 473(7346), 167-173.
  26. [26]  Klamka, J. (2009), Constrained controllability of semilinear systems with delays, Nonlinear Dynamics, 56(1), 169-177.
  27. [27]  Garniewicz, L., Ntouyas, S.K., and O'regan, D. (2005), Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces, Reports on Mathematical Physics, 56(3), 437-470.
  28. [28]  Shukla, A., Sukavanam, N., and Pandey, D.N. (2018), Approximate controllability of semilinear fractional stochastic control system, Asian-European Journal of Mathematics, 11(06), p.1850088.
  29. [29]  Ma, Y.K., Kavitha, K., Albalawi, W., Shukla, A., Nisar, K.S., and Vijayakumar, V. (2022), An analysis on the approximate controllability of Hilfer fractional neutral differential systems in Hilbert spaces, Alexandria Engineering Journal, 61(9), 7291-7302.
  30. [30]  Shukla, A., Sukavanam, N., and Pandey, D.N. (2015), Approximate controllability of semilinear stochastic control system with nonlocal conditions, Nonlinear Dynamical Systems Theory, 15(3), 321-333.
  31. [31]  Shukla, A., Sukavanam, N., and Pandey, D.N. (2016), Complete controllability of semilinear stochastic systems with delay in both state and control, Mathematical Reports (Bucuresti), 18, 247-259.
  32. [32]  Shukla, A., Sukavanam, N., and Pandey, D.N., (2015), Approximate Controllability of Semilinear Fractional Control Systems of Order $\alpha(1, 2]$, In 2015 Proceedings of the Conference on Control and its Applications, 175-180, Society for Industrial and Applied Mathematics.
  33. [33]  Raja, M.M., Vijayakumar, V., Shukla, A., Nisar, K.S., and Baskonus, H.M. (2022), On the approximate controllability results for fractional integrodifferential systems of order $1< r< 2$ with sectorial operators, Journal of Computational and Applied Mathematics, 415(2022), p.114492.
  34. [34]  Barnett, S. and Cameron, R. (1995), Introduction to Mathematical Control Theory, Oxford Applied Mathematics and Computing Science Series.
  35. [35]  Sakthivel, R., Samidurai, R., and Anthoni, S.M. (2010), Exponential stability for stochastic neural networks of neutral type with impulsive effects, Modern Physics Letters B, 24(11), 1099-1110.
  36. [36]  Mahmudov, N.I. (2003), Controllability of semilinear stochastic systems in Hilbert spaces, Journal of Mathematical Analysis and Applications, 288(1), 197-211.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates