[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Exact Controllability of Semi-linear Heterogeneous Networked Control Systems

Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 567--578 | DOI:10.5890/DNC.2026.12.007

Anil Singh Rathore$^{1}$, Om Prakash Singh$^{1}$, Arun Kumar Singh$^{2}$

$^{1}$ Department of Electronics and Communication Engineering, Amity School of Engineering & Technology, Amity University Uttar Pradesh, Lucknow Campus, Lucknow-206028, Uttar Pradesh, India

$^{2}$Department of Electronics Engineering, Rajkiya Engineering College, Kannauj-209732, Uttar Pradesh, India

Download Full Text PDF

 

Abstract

This paper investigates the controllability of networked systems with heterogeneous node-specific semilinear control systems. The nonlinearities are assumed to be Hölder continuous with bounded growth. A compact Kronecker-based formulation is developed to represent the system dynamics, and algebraic conditions are derived to ensure controllability under structural and dynamical heterogeneity. The analysis leverages fixed point theorems to guaranty the existence and uniqueness of solutions. The proposed framework generalizes classical PBH-based controllability results to include nonlinear effects and nonuniform actuation. Three illustrative examples - a bidirectional 2-node network, a 3-node ring, and a 3-node star with partial actuation-demonstrate the effectiveness of the proposed controllability conditions. This work contributes a rigorous and flexible extension of controllability theory for realistic semilinear networked control systems.

References

  1. [1]  Liu, Y.Y., Slotine, J.J., and Barabási, A.L. (2011), Controllability of complex networks, Nature, 473(7346), 167-173.
  2. [2]  Mesbahi, M. and Egerstedt, M. (2010), Graph theoretic methods in multiagent networks, Princeton University Press: Princeton.
  3. [3]  Antsaklis, P. and Baillieul, J. (2007), Special issue on technology of networked control systems, Proceedings of the IEEE, 95(1), 5-8.
  4. [4]  Kalman, R.E. (1960), Contributions to the theory of optimal control, Boletín de la Sociedad Matemática Mexicana, 5(2), 102-119.
  5. [5]  Sontag, E.D. (1998), Mathematical control theory, Springer: New York.
  6. [6]  Rugh, W.J. (1996), Linear system theory, Prentice-Hall: Englewood Cliffs, NJ.
  7. [7]  Zamani, M. and Lin, H. (2009), Structural controllability of multi-agent systems, In: Proceedings of the 2009 American Control Conference, pp. 5743-5748.
  8. [8]  Parlangeli, G. and Notarstefano, G. (2011), On the reachability and observability of path and cycle graphs, IEEE Transactions on Automatic Control, 57(3), 743-748.
  9. [9]  Olshevsky, A. (2014), Minimal controllability problems, IEEE Transactions on Control of Network Systems, 1(3), 249-258.
  10. [10]  Zhao, B., Chen, M.Z., Guan, Y., and Wang, L. (2017), Controllability of heterogeneous multi-agent networks, arXiv preprint arXiv:1708.02998.
  11. [11]  Pasqualetti, F., Zampieri, S., and Bullo, F. (2014), Controllability metrics, limitations and algorithms for complex networks, IEEE Transactions on Control of Network Systems, 1(1), 40-52.
  12. [12]  Trumpf, J. and Trentelman, H.L. (2018), Controllability and stabilizability of networks of linear systems, IEEE Transactions on Automatic Control, 64(8), 3391-3398.
  13. [13]  Wang, L., Wang, X., and Chen, G. (2017), Controllability of networked higher-dimensional systems with one-dimensional communication, Philosophical Transactions of the Royal Society A, 375, 20160215.
  14. [14]  Klamka, J. (2002), Controllability of nonlinear discrete systems, In: Proceedings of the 2002 American Control Conference, 6, pp. 4670-4671.
  15. [15]  Aubin, J.P. and Frankowska, H. (1990), Differential inclusions, Springer: Berlin.
  16. [16]  Deimling, K. (1985), Nonlinear functional analysis, Springer: Berlin.
  17. [17]  Lin, C.T. (1974), Structural controllability, IEEE Transactions on Automatic Control, 19(3), 201-208.
  18. [18]  Chapman, A. and Mesbahi, M. (2013), On strong structural controllability of networked systems: a constrained matching approach, In: Proceedings of the 2013 American Control Conference, pp. 6126-6131.
  19. [19]  Hao, Y., Wang, Q., Duan, Z., and Chen, G. (2019), Controllability of Kronecker product networks, Automatica, 110, 108597.
  20. [20]  Thomas, A., Ajayakumar, A., and George, R.K. (2025), Controllability and observability of heterogeneous networked systems with non-uniform node dimensions and distinct inner-coupling matrices, IEEE Open Journal of Control Systems.
  21. [21]  Ajayakumar, A. and George, R.K. (2023), Controllability of networked systems with heterogeneous dynamics, Mathematics of Control, Signals, and Systems, 35(2), 307-326.
  22. [22]  Ajayakumar, A. and George, R.K. (2023), Controllability of a class of heterogeneous networked systems, Foundations, 3(2), 167-180.
  23. [23]  Ajayakumar, A. and George, R.K. (2022), A note on controllability of directed networked MIMO systems with heterogeneous dynamics, IEEE Transactions on Control of Network Systems, 10(2), 575-578.
  24. [24]  Boyd, D.W. and Wong, J.S. (1969), On nonlinear contractions, Proceedings of the American Mathematical Society, 20(2), 458-464.
  25. [25]  Zeidler, E. (1986), Nonlinear functional analysis and its applications I: fixed-point theorems, Springer-Verlag: New York.
  26. [26]  Sweis, H., Abu Arqub, O., and Shawagfeh, N. (2024), Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer $(\alpha,\beta)$-framework set, PLOS ONE, 19(6), e0305259.
  27. [27]  Sweis, H., Shawagfeh, N., and Arqub, O.A. (2022), Fractional crossover delay differential equations of Mittag-Leffler kernel: existence, uniqueness, and numerical solutions using the Galerkin algorithm based on shifted Legendre polynomials, Results in Physics, 41, 105891.
  28. [28]  Sweis, H., Arqub, O.A., and Shawagfeh, N. (2023), Fractional delay integrodifferential equations of nonsingular kernels: existence, uniqueness, and numerical solutions using Galerkin algorithm based on shifted Legendre polynomials, International Journal of Modern Physics C, 34(04), 2350052.
  29. [29]  Fen, M.O. and Fen, F.T. (2021), Unpredictable oscillations of SICNNs with delay, Neurocomputing, 464, 119-129.
  30. [30]  Fen, M.O. and Fen, F.T. (2022), Replication of period-doubling route to chaos in coupled systems with delay, Filomat, 36(2), 599-613.
  31. [31]  Fen, M.O. and Tokmak Fen, F. (2025), Continuous-time and discrete-time quasilinear systems with asymptotically unpredictable solutions, Mediterranean Journal of Mathematics, 22(6), 1-19.

Copyright © 2011-2026 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates