Skip to main content
SpringerLink
Log in

Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this article, we are interested in the fixed-time stabilization (FTSt) and fixed-time synchronization (FTSy) of a class of inertial neural networks with time-varying and distributed delays. To obtain FTSt and FTSy, sliding mode controllers are developed based on sliding mode control techniques and by using sliding variables. Two polynomial feedback control laws are exploited to achieve the FTSt and the FTSy but they are singular. To get rid of the singularities, the saturation function is used into the design of the controllers and the almost FTSt and almost FTSy are proved. Finally, numerical examples are presented to show the effectiveness of the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Alimi AM, Aouiti C, Assali EA (2019) Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 332:29–43

    Article  Google Scholar 

  2. Alimi AM, Aouiti C, Chérif F, Dridi F, M’hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing 321:274–295

    Article  Google Scholar 

  3. Aouiti C, Alimi AM, Karray F, Maalej A (2005) The design of beta basis function neural network and beta fuzzy systems by a hierarchical genetic algorithm. Fuzzy Sets Syst 154(2):251–274

    Article  MathSciNet  MATH  Google Scholar 

  4. Aouiti C, Alimi AM, Maalej A (2002) A genetic-designed beta basis function neural network for multi-variable functions approximation. Syst Anal Modell Simul 42(7):975–1009

    Article  MATH  Google Scholar 

  5. Aouiti C, Assali EA (2019) Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 31(11):7781–7803

    Article  Google Scholar 

  6. Aouiti C, Assali EA, Cao J, Alsaedi A (2018) Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays. Int J Syst Sci 49(10):2202–2214

    Article  MathSciNet  Google Scholar 

  7. Aouiti C, Ben Gharbia I, Cao J, M’hamdi MS, Alsaedi A (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111–127

    Article  MathSciNet  MATH  Google Scholar 

  8. Aouiti C, Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260:378–392

    Article  Google Scholar 

  9. Aouiti C, Hui Q, Jallouli H, Moulay E (2020) Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2020.10.018

    Article  Google Scholar 

  10. Aouiti C, Li X, Miaadi F (2018) A new LMI approach to finite and fixed time stabilization of high-order class of BAM neural networks with time-varying delays. Neural Process Lett 50:1–24

    Google Scholar 

  11. Aouiti C, M’hamdi MS, Chérif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46(2):487–506

    Article  Google Scholar 

  12. Aouiti C, M’hamdi MS, Chérif F, Alimi AM (2017) Impulsive generalised high-order recurrent neural networks with mixed delays: stability and periodicity. Neurocomputing 321:296–307

    Article  Google Scholar 

  13. Aouiti C, Xiaodi L, Miaadi F (2018) Finite time stabilization of uncertain delayed Hopfield neural networks with a time-varying leakage delay via non-chattering control. Sci China Technol Sci 62:1111–1122

    Article  Google Scholar 

  14. Aquino G, Rubio JDJ, Pacheco J, Gutierrez GJ, Ochoa G, Balcazar R, Cruz DR, Garcia E, Novoa JF, Zacarias A (2020) Novel nonlinear hypothesis for the delta parallel robot modeling. IEEE Access 8:46324–46334

    Article  Google Scholar 

  15. Blekhman II, Fradkov AL, Tomchina OP, Bogdanov D (2002) Self-synchronization and controlled synchronization: general definition and example design. Math Comput Simul 58(4–6):367–384

    Article  MathSciNet  MATH  Google Scholar 

  16. Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60(3):032201

    Article  MathSciNet  Google Scholar 

  17. Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172

    Article  MATH  Google Scholar 

  18. Chen Z, Zhang B, Stojanovic V, Zhang Y, Zhang Z (2020) Event-based fuzzy control for ts fuzzy networked systems with various data missing. Neurocomputing 417:322–332

    Article  Google Scholar 

  19. Cheng P, Chen M, Stojanovic V, He S (2021) Asynchronous fault detection filtering for piecewise homogenous markov jump linear systems via a dual hidden markov model. Mech Syst Signal Process 151:107353

    Article  Google Scholar 

  20. Chiang H-S, Chen M-Y, Huang Y-J (2019) Wavelet-based EEG processing for epilepsy detection using fuzzy entropy and associative petri net. IEEE Access 7:103255–103262

    Article  Google Scholar 

  21. Cui N, Jiang H, Hu C, Abdurahman A (2018) Global asymptotic and robust stability of inertial neural networks with proportional delays. Neurocomputing 272:326–333

    Article  Google Scholar 

  22. de Jesús Rubio J (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuzzy Syst 17(6):1296–1309

    Article  Google Scholar 

  23. de Rubio JJ (2020) Stability analysis of the modified Levenberg–Marquardt algorithm for the artificial neural network training. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3015200

    Article  Google Scholar 

  24. DeCarlo RA, Zak SH, Matthews GP (1988) Variable structure control of nonlinear multivariable systems: a tutorial. Proc IEEE 76(3):212–232

    Article  Google Scholar 

  25. Du H, Li S, Qian C (2011) Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Autom Control 56(11):2711–2717

    Article  MathSciNet  MATH  Google Scholar 

  26. Forti M, Nistri P, Quincampoix M (2004) Generalized neural network for nonsmooth nonlinear programming problems. IEEE Trans Circuits Syst I Regul Pap 51(9):1741–1754

    Article  MathSciNet  MATH  Google Scholar 

  27. Gan Q, Xu R, Yang P (2012) Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control. Commun Nonlinear Sci Numer Simul 17(1):433–443

    Article  MathSciNet  MATH  Google Scholar 

  28. Graham JH, Zurada JM (1996) A neural network approach for safety and collision avoidance in robotic systems. Reliab Eng Syst Saf 53(3):327–338

    Article  Google Scholar 

  29. Guo Z, Gong S, Huang T (2018) Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control. Neurocomputing 293:100–107

    Article  Google Scholar 

  30. Hernández G, Zamora E, Sossa H, Téllez G, Furlán F (2020) Hybrid neural networks for big data classification. Neurocomputing 390:327–340

    Article  Google Scholar 

  31. Huang C, Cao J, Xiao M, Alsaedi A, Alsaadi FE (2017) Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders. Appl Math Comput 293:293–310

    MathSciNet  MATH  Google Scholar 

  32. Huang W, Lai KK, Nakamori Y, Wang S, Yu L (2007) Neural networks in finance and economics forecasting. Int J Inf Technol Decis Mak 6(01):113–140

    Article  Google Scholar 

  33. Jiang B, Hu Q, Friswell MI (2016) Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Trans Control Syst Technol 24(5):1892–1898

    Article  Google Scholar 

  34. Kisel’ák J, Lu Y, Švihra J, Szépe P, Stehlík M (2020) “SPOCU”: scaled polynomial constant unit activation function. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05182-1

    Article  Google Scholar 

  35. Kosmatopoulos EB, Polycarpou MM, Christodoulou MA, Ioannou PA (1995) High-order neural network structures for identification of dynamical systems. IEEE Trans Neural Netw 6(2):422–431

    Article  Google Scholar 

  36. Lee S-K, Jang D (1996) Translation, rotation and scale invariant pattern recognition using spectral analysis and hybrid genetic-neural-fuzzy networks. Comput Ind Eng 30(3):511–522

    Article  Google Scholar 

  37. Li H, Li C, Huang T, Zhang W (2018) Fixed-time stabilization of impulsive Cohen–Grossberg BAM neural networks. Neural Netw 98:203–211

    Article  MATH  Google Scholar 

  38. Li R, Cao J (2018) Finite-time and fixed-time stabilization control of delayed memristive neural networks: robust analysis technique. Neural Process Lett 47(3):1077–1096

    Article  MathSciNet  Google Scholar 

  39. Li R, Cao J, Alsaedi A, Ahmad B, Alsaadi FE, Hayat T (2016) Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks. Complexity 21(S2):459–469

    Article  MathSciNet  Google Scholar 

  40. Li S, Ahn CK, Xiang Z (2019) Adaptive fuzzy control of switched nonlinear time-varying delay systems with prescribed performance and unmodeled dynamics. Fuzzy Sets Syst 371:40–60

    Article  MathSciNet  MATH  Google Scholar 

  41. Li S, Ahn CK, Xiang Z (2020) Command Filter based adaptive fuzzy finite-time control for switched nonlinear systems using state-dependent switching method. IEEE Trans Fuzzy Syst 2020:1. https://doi.org/10.1109/TFUZZ.2020.2965917

    Article  Google Scholar 

  42. Liu Q, Liao X, Guo S, Wu Y (2009) Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal Real World Appl 10(4):2384–2395

    Article  MathSciNet  MATH  Google Scholar 

  43. Liu Y, Yue H, Wang W (2018) Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics. In: 12th International conference on control (CONTROL). IEEE, pp 324–329

  44. Malmgren H, Borga M, Niklasson L (2012) Artificial neural networks in medicine and biology: proceedings of the ANNIMAB-1 conference, Göteborg, Sweden, 13–16 May 2000. Springer, Berlin

  45. Meda-Campaña JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968–31973

    Article  Google Scholar 

  46. Mhamdi MS, Aouiti C, Touati A, Alimi AM, Snasel V (2016) Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci 36(6):1662–1682

    Article  MathSciNet  MATH  Google Scholar 

  47. Moulay E, Perruquetti W (2006) Finite time stability and stabilization of a class of continuous systems. J Math Anal Appl 323(2):1430–1443

    Article  MathSciNet  MATH  Google Scholar 

  48. Ni J, Liu L, Liu C, Hu X, Li S (2016) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155

    Google Scholar 

  49. Papik K, Molnar B, Schaefer R, Dombovari Z, Tulassay Z, Feher J (1998) Application of neural networks in medicine—a review. Med Sci Monit 4(3):MT538–MT546

    Google Scholar 

  50. Parsegov S, Polyakov A, Shcherbakov P (2013) Fixed-time consensus algorithm for multi-agent systems with integrator dynamics. IFAC Proc Vol 46(27):110–115

    Article  Google Scholar 

  51. Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    Article  MathSciNet  MATH  Google Scholar 

  52. Rajchakit G, Pratap A, Raja R, Cao J, Alzabut J, Huang C (2019) Hybrid control scheme for projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks with mixed delays. Mathematics 7(8):759

    Article  Google Scholar 

  53. Savković-Stevanović J (1993) A neural network model for analysis and optimization of processes. Comput Chem Eng 17:S411–S416

    Article  Google Scholar 

  54. Shi Y, Zhu P, Qin K (2014) Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller. Neurocomputing 123:443–449

    Article  Google Scholar 

  55. Stojanovic V, He S, Zhang B (2020) State and parameter joint estimation of linear stochastic systems in presence of faults and non-Gaussian noises. Int J Robust Nonlinear Control 30(16):6683–6700

    Article  MathSciNet  Google Scholar 

  56. Tong S, Li Y (2010) Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci China Inf Sci 53(2):307–324

    Article  MathSciNet  Google Scholar 

  57. Tong S, Min X, Li Y (2020) Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Trans Cybern 50:3903–3913. https://doi.org/10.1109/TCYB.2020.2977175

    Article  Google Scholar 

  58. Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222

    Article  MathSciNet  MATH  Google Scholar 

  59. Utkin V, Guldner J, Shi J (2009) Sliding mode control in electro-mechanical systems, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  60. Wheeler DW, Schieve W (1997) Stability and chaos in an inertial two-neuron system. Physica D Nonlinear Phenom 105(4):267–284

    Article  MATH  Google Scholar 

  61. Wu W, Zhou W, Chen T (2008) Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans Circuits Syst I Regul Pap 56(4):829–839

    Article  MathSciNet  Google Scholar 

  62. Xi X, Mobayen S, Ren H, Jafari S (2018) Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control. J Vib Control 24(17):3842–3854

    Article  MathSciNet  Google Scholar 

  63. Xiong J-J, Zhang G-B, Wang J-X, Yan T-H (2019) Improved sliding mode control for finite-time synchronization of nonidentical delayed recurrent neural networks. IEEE Trans Neural Netw Learn Syst 31(6):2209–2216

    Article  MathSciNet  Google Scholar 

  64. Yang F, Mei J, Wu Z (2016) Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control. IET Control Theory Appl 10(14):1630–1640

    Article  MathSciNet  Google Scholar 

  65. Yang T (2004) A survey of chaotic secure communication systems. Int J Comput Cognit 2(2):81–130

    Google Scholar 

  66. Young KD, Utkin VI, Ozguner U (1996) A control engineer’s guide to sliding mode control. In: IEEE International workshop on variable structure systems (VSS’96). IEEE, pp 1–14

  67. Yunquan K, Chunfang M (2013) Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput Appl 23(3–4):1089–1099

    Article  Google Scholar 

  68. Zhang D, Xu J (2010) Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller. Appl Math Comput 217(1):164–174

    Article  MathSciNet  MATH  Google Scholar 

  69. Zhang W (2010) Computational ecology: artificial neural networks and their applications. World Scientific, Singapore

    Book  MATH  Google Scholar 

  70. Zhang W, Tang Y, Miao Q, Fang J-A (2013) Synchronization of stochastic dynamical networks under impulsive control with time delays. IEEE Trans Neural Netw Learn Syst 25(10):1758–1768

    Article  Google Scholar 

  71. Zhang X, Shuping H, Stojanovic V, Luan X, Liu F (2020) Finite-time asynchronous dissipative filtering of conic-type nonlinear markov jump systems. Sci China Inform Sci. 5:8–9. https://doi.org/10.1007/s11432-020-2913-x

    Article  Google Scholar 

  72. Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151:1316–1326

    Article  Google Scholar 

  73. Zhao Z-S, Zhang J, Sun L-K (2013) Sliding mode control in finite time stabilization for synchronization of chaotic systems. Int Sch Res Not 2013:320180. https://doi.org/10.1155/2013/320180

    Article  MATH  Google Scholar 

  74. Zhou L, Tao H, Paszke W, Stojanovic V, Yang H (2020) Pd-type iterative learning control for uncertain spatially interconnected systems. Mathematics 8(9):1528

    Article  Google Scholar 

  75. Zuo Z, Defoort M, Tian B, Ding Z (2016) Fixed-time stabilization of second-order uncertain multivariable nonlinear systems. In: 35th Chinese control conference (CCC). IEEE, pp 907–912

  76. Zuo Z, Han Q-L, Ning B, Ge X, Zhang X-M (2018) An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Ind Inform 14(6):2322–2334

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, BP W, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Hediene Jallouli

  2. Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0511, USA

    Qing Hui

  3. XLIM (UMR CNRS 7252), Université de Poitiers, 11 bd Marie et Pierre Curie, 86073, Poitiers Cedex 9, France

    Emmanuel Moulay

Authors
  1. Chaouki Aouiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qing Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hediene Jallouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Emmanuel Moulay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaouki Aouiti.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., Hui, Q., Jallouli, H. et al. Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays. Neural Comput & Applic 33, 11555–11572 (2021). https://doi.org/10.1007/s00521-021-05833-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-05833-x

Keywords

Search

Navigation