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A Robust Non-Fragile Control Lag Synchronization for Fractional Order Multi-Weighted Complex Dynamic Networks with Coupling Delays

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Abstract

This problem addresses the fractional order lag synchronization for multi-weighted complex dynamical networks with coupling delays via non-fragile control. Establishing a general multi-weighted complex network model including the coupling delays with external disturbances and investigates the lag synchronization criteria using the state feedback non-fragile control. Based on the Lyapunov stability theorem and comparison principle, we ensured our model guarantees the lag synchronization under the controller. The effectiveness of the proposed work is shown in numerical simulations with examples.

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References

  1. Kilbas AAA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier Science Limited, Amsterdam

    MATH  Google Scholar 

  2. Pratap A, Raja R, Agarwal RP (2020) Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem. Neural Process Lett 51:2453–2479

    Article  Google Scholar 

  3. Pratap A, Raja R, Cao J, Rihan Fathalla A., Seadawy Aly R. (2020) Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations. Chaos Solitons Fract 131:109–491

    Article  MathSciNet  MATH  Google Scholar 

  4. Pratap A, Raja R, Cao J (2020) Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks. Adv Diff Eqs 97:1–24

    MATH  Google Scholar 

  5. Pratap A, Raja R, Alzabut J, Cao J, Rajchakit G, Huang C (2020) Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. Math Methods Appl Sci 43(10):6223–6253

    Article  MathSciNet  MATH  Google Scholar 

  6. Pratap A, Raja R, Sowmiya C, Bagdasar O, Cao J, Rajchakit G (2020) Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays. Asian J Control 22(1):570–583

    Article  MathSciNet  Google Scholar 

  7. Moser BK (1996) 1 - Linear algebra and related introductory topics, Linear Models Academic Press pp 1–22

  8. Kaviarasan B, Kwon OM, Park MJ (2020) Composite synchronization control for delayed coupling complex dynamical networks via a disturbance observer-based method. Nonlinear Dyn 99:1601–1619

    Article  MATH  Google Scholar 

  9. Zhang C, Shi L (2019) Exponential synchronization of stochastic complex networks with multi-weights: a graph-theoretic approach. J Franklin Inst 356(7):4106–4123

    Article  MathSciNet  MATH  Google Scholar 

  10. Li C, Liao X, Wong K (2004) Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication. Physica D 194(3–4):187–202

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang D, Sun S, Zhao H, Yang J (2020) Laser Doppler signal processing based on trispectral interpolation of Nuttall window. Optik 205:163364

    Article  Google Scholar 

  12. Wang F, Zheng Z, Yang Y (2019) Synchronization of complex dynamical networks with hybrid time delay under event-triggered control: the threshold function method. Complexity 2019:17

    MATH  Google Scholar 

  13. Kong F, Zhu Q (2021) New fixed-time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov-Krasovskii functional method. Int J Robust Nonlinear Control 31:471–495

    Article  MathSciNet  Google Scholar 

  14. Kong F, Zhu Q, Sakthivel R, Mohammadzadeh A (2021) Fixed-time synchronization analysis for discontinuous fuzzy inertial neural networks with parameter uncertainties. Neurocomputing 422:295–313

    Article  Google Scholar 

  15. Gaba GS, Kumar G, Kim T, Monga H, Kumar Secure P (2021) Device-to-Device communications for 5G enabled Internet of Things applications. Comput Commun 169:114–128

    Article  Google Scholar 

  16. Liu H, Lu JA, Lu J, Hill DJ (2009) Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45(8):1799–1807

    Article  MathSciNet  MATH  Google Scholar 

  17. Jia J, Zeng Z (2020) LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control. Neurocomputing 412:226–243

    Article  Google Scholar 

  18. Grigorenko I, Grigorenko E (2003) Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 91(3):34–101

    Article  Google Scholar 

  19. Podlubny I (1999) Fractional differential equations. Academic Press, San Diego, California, p 198

    MATH  Google Scholar 

  20. Langville A, Stewart W (2004) The Kronecker product and stochastic automata networks. J Comput Appl Math 167:429–447

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen L, Chai Y, Wu R (2011) Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems. Phys Lett A 375(21):2099–2110

    Article  MATH  Google Scholar 

  22. Zhang L, Yang Y, wang F, sui X (2018) Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch. J Franklin Inst 355(3):1217–1240

    Article  MathSciNet  MATH  Google Scholar 

  23. Imran Shahid M, Ling Q (2020) Event-triggered distributed dynamic output-feedback dissipative control of multi-weighted and multi-delayed large-scale systems. ISA Trans 96:116–131

    Article  MATH  Google Scholar 

  24. Ali MS, Usha M, Zhu Q, Shanmugam S (2020) Synchronization analysis for stochastic T-S fuzzy complex networks with Markovian jumping parameters and mixed time-varying delays via impulsive control. Math Probl Eng 2020:27

    Article  MathSciNet  MATH  Google Scholar 

  25. Selvaraj P, Sakthivel R, Kwon OM (2018) Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation. Nonlinear Dyn 94:3101–3116

    Article  MATH  Google Scholar 

  26. Sakthivel R, Sakthivel R, Kwon OM (2019) Observer-based robust synchronization of fractional-order multi-weighted complex dynamical networks. Nonlinear Dyn 98:1231–1246

    Article  Google Scholar 

  27. Sakthivel R, Sakthivel R, Kwon Om, Kaviarasan B (2021) Fault estimation and synchronization control for complex dynamical networks with time-varying coupling delay. Int J Robust Nonlinear Control 31:2205–2221

    Article  MathSciNet  Google Scholar 

  28. Liang S, Wu R, Chen L (2015) Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays. Neurocomputing 168:618–625

    Article  Google Scholar 

  29. Qiu S, Huang Y, Ren S (2018) Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay. Neurocomputing 275:1250–1260

    Article  Google Scholar 

  30. Lopez-Garcia TB, Coronado-Mendoza A, Domínguez-Navarro JA (2020) Artificial neural networks in microgrids: a review. Eng Appl Artif Intell 95:14

    Article  Google Scholar 

  31. Saravanakumar T, Muoi NH, Zhu Q (2020) Finite-time sampled-data control of switched stochastic model with non-deterministic actuator faults and saturation nonlinearity. J Franklin Inst 357(18):13637–13665

    Article  MathSciNet  MATH  Google Scholar 

  32. Cao W, Zhu Q (2021) Razumikhin-type theorem for pth exponential stability of impulsive stochastic functional differential equations based on vector Lyapunov function. Nonlinear Anal Hybrid Syst 39:10

    Article  MathSciNet  MATH  Google Scholar 

  33. Guo W (2011) Lag synchronization of complex networks via pinning control. Nonlinear Anal Real World Appl 12(5):2579–2585

    Article  MathSciNet  MATH  Google Scholar 

  34. Yu W, Cao J (2007) Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Phys A 375(2):467–482

    Article  Google Scholar 

  35. Zhang W, Cao J, Wu R, Alsaadi FE, Alsaedi A (2019) Lag projective synchronization of fractional-order delayed chaotic systems. J Franklin Inst 356(3):1522–1534

    Article  MathSciNet  MATH  Google Scholar 

  36. An X, Zhang L (2020) A new complex network model with multi-weights and its synchronization control. Adv Math Phys 2020:12

    Google Scholar 

  37. Song X, Song S, Li B (2018) Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications. Trans Inst Meas Control 40(10):3078–3087

    Article  Google Scholar 

  38. Zhang X, Wang J, Huang Y, Ren S (2018) Analysis and pinning control for passivity of multi-weighted complex dynamical networks with fixed and switching topologies. Neurocomputing 275:958–968

    Article  Google Scholar 

  39. Huang Y, Hou J, Yang E (2020) General decay lag anti-synchronization of multi-weighted delayed coupled neural networks with reaction-diffusion terms. Inf Sci 511:36–57

    Article  MathSciNet  MATH  Google Scholar 

  40. Jia Y, Wu H, Cao J (2020) Non-fragile robust finite-time synchronization for fractional-order discontinuous complex networks with multi-weights and uncertain couplings under asynchronous switching. Appl Math Comput 370:124–929

    MathSciNet  MATH  Google Scholar 

  41. Zhao Y, Zhu Q (2021) Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays. Int J Robust Nonlinear Control 2021:1–20

    MathSciNet  Google Scholar 

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Acknowledgements

This work was jointly supported by the RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRS-I/2016(SAP-I) and DST (FIST- Phase I) vide letter No.SR/FIST/MS-I/2018-17, the National Science Centre in Poland Grant DEC-2017/25/B/ST7/02888, J. Alzabut would like to thank Prince Sultan University, Saudi Arabia and OSTIM University, Ankara, Turkey and the National Natural Science Foundation of China (62173139), the Science and Technology Innovation Program of Hunan Province (2021RC4030), Hunan Provincial Science and Technology Project Foundation (2019RS1033).

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Authors and Affiliations

  1. Department of Mathematics, Alagappa University, Karaikudi, 630 004, India

    S. Aadhithiyan

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  3. School of Mathematics and Statistics, Hunan Normal University, Hunan, 410081, People’s Republic of China

    Q. Zhu

  4. School of Electronic Information and Electrical Engineering, Chengdu University, Sichuan Chengdu, 610106, P.R. China

    Q. Zhu

  5. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia

    J. Alzabut

  6. Department of Industrial Engineering, OSTİM Technical University, Ankara, 06374, Turkey

    J. Alzabut

  7. Faculty of Automatic Control, Electronics and Computer Science, Department of Automatic Control, and Robotics, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    M. Niezabitowski

  8. Institute for Intelligent System Research and Innovation, Deakin University, Geelong, Australia

    C. P. Lim

Authors
  1. S. Aadhithiyan
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  2. R. Raja
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  3. Q. Zhu
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  4. J. Alzabut
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  5. M. Niezabitowski
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  6. C. P. Lim
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Correspondence to Q. Zhu.

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Aadhithiyan, S., Raja, R., Zhu, Q. et al. A Robust Non-Fragile Control Lag Synchronization for Fractional Order Multi-Weighted Complex Dynamic Networks with Coupling Delays. Neural Process Lett 54, 2919–2940 (2022). https://doi.org/10.1007/s11063-022-10747-3

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